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Journal articles on the topic 'Analytic perturbations'

Author: Grafiati

Published: 25 May 2023

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1

Lewowicz, Jorge, and Eduardo Lima De Sá. "Analytic models of pseudo-Anosov maps." Ergodic Theory and Dynamical Systems 6, no. 3 (September 1986): 385–92. http://dx.doi.org/10.1017/s0143385700003564.

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AbstractWe give a new proof of the existence of analytic models of pseudo-Anosov maps. The persistence properties of Thurston's maps ensure that any Co-perturbation of them presents all their dynamical features. Using Lyapunov functions of two variables we are able to choose certain analytic perturbations which do not add any new dynamical behaviour to the original pseudo-Anosov map.

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2

Inomata, Keisuke. "Analytic solutions of scalar perturbations induced by scalar perturbations." Journal of Cosmology and Astroparticle Physics 2021, no. 03 (March 9, 2021): 013. http://dx.doi.org/10.1088/1475-7516/2021/03/013.

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3

Oharu, Shinnosuke. "Nonlinear perturbations of analytic semigroups." Semigroup Forum 42, no. 1 (December 1991): 127–46. http://dx.doi.org/10.1007/bf02573415.

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4

Veloz, Tomas, Pedro Maldonado, Evo Bussseniers, Alejandro Bassi, Shima Beigi, Marta Lenartowicz, and Francis Heylighen. "Towards an Analytic Framework for System Resilience Based on Reaction Networks." Complexity 2022 (January 31, 2022): 1–29. http://dx.doi.org/10.1155/2022/9944562.

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Reaction network is a promising framework for representing complex systems of diverse and even interdisciplinary types. In this approach, complex systems appear as self-maintaining structures emerging from a multitude of interactions, similar to proposed scenarios for the origin of life out of autocatalytic networks. The formalism of chemical organization theory (COT) mathematically specifies under which conditions a reaction network is stable enough to be observed as a whole complex system. Such conditions specify the notion of organization, crucial in COT. In this paper, we show that the structure and operation of organizations can be advanced towards a formal framework of resilience in complex systems. That is, we show that there exist three fundamental types of change (state, process, and structural) defined for reaction networks, and that these perturbations not only provide a general representation of perturbations in the context of resilience but also pave the ground to formalize different forms of resilient responses. In particular, we show that decomposing the network’s operational structure into dynamically decoupled modules allows to formalize what is the impact of a perturbation and to what extent any potential compensation to that perturbation will be successful. We illustrate our approach with a toy model of a farm that operates in a sustainable way producing milk, eggs, and/or grains from other resources. With the help of simulations, we analyze the different types of perturbations and responses that the farm can undergo and how that affects its sustainable operation.

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5

KODAMA, HIDEO, and MISAO SASAKI. "EVOLUTION OF ISOCURVATURE PERTURBATIONS I: PHOTON-BARYON UNIVERSE." International Journal of Modern Physics A 01, no. 01 (April 1986): 265–301. http://dx.doi.org/10.1142/s0217751x86000137.

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The isocurvature perturbation in the photon-baryon universe is comprehensively studied by analytic methods in the framework of the gauge-invariant perturbation theory. In particular the evolutionary behavior of the isocurvature perturbation and its influence on the anisotropy in the cosmic microwave background are examined in detail. The results are compared with those for the adiabatic perturbation and some peculiar features of the isocurvature perturbation are pointed out and their origin is clarified. Besides these studies the ambiguities associated with the definition of non-adiabatic perturbations, especially the so-called isothermal perturbation are critically discussed and a clear definition of isocurvature perturbation is given.

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6

DE SIMONE, EMILIANO. "A RENORMALIZATION PROOF OF THE KAM THEOREM FOR NON-ANALYTIC PERTURBATIONS." Reviews in Mathematical Physics 19, no. 06 (July 2007): 639–75. http://dx.doi.org/10.1142/s0129055x07003085.

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We shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non-analytic perturbation (the latter will be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which the perturbations are analytic approximations of the original one. We shall finally show that the sequence of the approximate solutions will converge to a differentiable solution of the original problem.

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7

Nusser, A. "Analytic solutions for coupled linear perturbations." Monthly Notices of the Royal Astronomical Society 317, no. 4 (October 1, 2000): 902–6. http://dx.doi.org/10.1046/j.1365-8711.2000.03708.x.

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8

Bonnans, Joseph Frédéric, Eduardo Casas, and Miguel Lobo. "Analytic singular perturbations of elliptic systems." Journal of Mathematical Analysis and Applications 122, no. 2 (March 1987): 422–26. http://dx.doi.org/10.1016/0022-247x(87)90271-x.

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9

DE COSTER, C., and K. HEYDE. "F-SPIN SYMMETRY BREAKING: APPLICATION TO THE U(5) AND SU(3) LIMIT." International Journal of Modern Physics A 04, no. 15 (September 1989): 3907–38. http://dx.doi.org/10.1142/s0217751x8900159x.

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Starting from the U(5) and SU(3) dynamic symmetries, perturbations on an F-spin scalar IBM-2 Hamiltonian are studied. The parameters describing the perturbations are chosen such as to introduce only the F-spin vector and the F-spin tensor terms of rank two. Effects on the F-spin structure of the wave functions, excitation energies and electromagnetic transition probabilities are studied for the lowest symmetric and mixed-symmetry states. If possible, numerical results are compared to analytic expressions derived via the first-order perturbation calculations.

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10

Park, Chan. "Observation of Gravitational Waves by Invariants for Electromagnetic Waves." Astrophysical Journal 940, no. 1 (November 1, 2022): 58. http://dx.doi.org/10.3847/1538-4357/ac9bff.

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Abstract We lay a theoretical foundation in the observation of gravitational waves (GWs) by electromagnetic waves (EMWs) performing a full electromagnetic analysis without any optical approximation. For that, the perturbation of plane EMWs is obtained by solving the perturbed Maxwell equation with GWs in the Minkowski background spacetime. In a GW detector using the EMWs, we propose to measure the electromagnetic invariants that are independent of the motion of the EMW receiver and whose perturbations are gauge-invariant. Imposing a physical boundary condition at EMW emitters, we have analytic results for the perturbations of invariants that can be measured in the EMW receiver. Finally, we show antenna patterns of the detector with monochromatic plane GWs and EMWs.

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11

Magnus, R. J. "On perturbations of a translationally-invariant differential equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 110, no. 1-2 (1988): 1–25. http://dx.doi.org/10.1017/s0308210500024811.

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SynopsisWe study certain perturbations of the differential equation Δu − u + up = 0 on all of n-dimensional Euclidean space. Conditions are obtained which ensure the existence of a solution to the perturbed equation near a given solution to the unperturbed equation. We have to overcome degeneracy of the unperturbed solution and lack of smooth dependence on the perturbation parameter. An abstract version of the argument is sketched in a functional-analytic setting related toequivariant bifurcation theory. We consider also a smooth perturbation with several parameters and study the singularities of the mapping which maps each solution to its associated parameters.

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12

Hassan, MR, and RR Thapa. "Periodic Solution of the restricted three body problem." BIBECHANA 10 (December 12, 2013): 44–51. http://dx.doi.org/10.3126/bibechana.v10i0.9310.

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The effect of perturbation in centrifugal force on the periodic solution of the restricted three-body problem representing analytic continuation of Keplerian rectilinear periodic motion has been examined. However, we have taken the perturbation in the centrifugal force to be of the order of μ, the reduced mass of the smaller primary. We have calculated the first order perturbations also. BIBECHANA 10 (2014) 44-51 DOI: http://dx.doi.org/10.3126/bibechana.v10i0.9310

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13

Holder, A. "Simultaneous Data Perturbations and Analytic Center Convergence." SIAM Journal on Optimization 14, no. 3 (January 2004): 841–68. http://dx.doi.org/10.1137/s1052623402409319.

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14

Hu, Wayne, and Naoshi Sugiyama. "Small‐Scale Cosmological Perturbations: An Analytic Approach." Astrophysical Journal 471, no. 2 (November 10, 1996): 542–70. http://dx.doi.org/10.1086/177989.

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15

Ran, A. C. M., and L. Rodman. "Semidefinite perturbations of analytic Hermitian matrix functions." Integral Equations and Operator Theory 12, no. 5 (September 1989): 739–45. http://dx.doi.org/10.1007/bf01194561.

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16

SCHWARZ, DOMINIK J. "ANALYTIC SOLUTIONS FOR COSMOLOGICAL PERTURBATIONS IN MULTI-DIMENSIONAL SPACE-TIME." International Journal of Modern Physics D 03, no. 01 (March 1994): 265–68. http://dx.doi.org/10.1142/s0218271894000423.

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We obtain analytic solutions for the density contrast and the anisotropic pressure in a multi-dimensional FRW cosmology with collisionless, massless matter. These are compared with perturbations of a perfect fluid universe. To describe the metric perturbations we use manifest gauge invariant metric potentials. The matter perturbations are calculated by means of (automatically gauge invariant) finite temperature field theory, instead of kinetic theory.

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17

STENLUND, MIKKO. "CONSTRUCTION OF WHISKERS FOR THE QUASIPERIODICALLY FORCED PENDULUM." Reviews in Mathematical Physics 19, no. 08 (September 2007): 823–77. http://dx.doi.org/10.1142/s0129055x07003127.

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We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, giving a simple construction of unstable KAM tori and their stable and unstable manifolds for analytic perturbations. We extend analytically the solutions of the equations of motion, order by order in the perturbation parameter, to a uniform neighborhood of the time axis.

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18

Aiena, P., and M. Kachad. "Property $$(UW{\scriptstyle \Pi })$$ under perturbations." Annals of Functional Analysis 11, no. 1 (December 1, 2019): 29–46. http://dx.doi.org/10.1007/s43034-019-00013-4.

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AbstractProperty $$(UW {\scriptstyle \Pi })$$(UWΠ), introduced in Berkani and Kachad (Bull Korean Math Soc 49:1027–1040, 2015) and studied more recently in Aiena and Kachad (Acta Sci Math (Szeged) 84:555–571, 2018) may be thought as a variant of Browder’s theorem, or Weyl’s theorem, for bounded linear operators acting on Banach spaces. In this article we study the stability of this property under some commuting perturbations, as quasi-nilpotent perturbation and, more in general, under Riesz commuting perturbations. We also study the transmission of property $$(UW {\scriptstyle \Pi })$$(UWΠ) from T to f(T), where f is an analytic function defined on a neighborhood of the spectrum of T. Furthermore, it is shown that this property is transferred from a Drazin invertible operator T to its Drazin inverse S.

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19

Forni, Giovanni. "Analytic destruction of invariant circles." Ergodic Theory and Dynamical Systems 14, no. 2 (June 1994): 267–98. http://dx.doi.org/10.1017/s0143385700007872.

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20

Kapitula, Todd. "Bifurcating bright and dark solitary waves for the perturbed cubic-quintic nonlinear Schrödinger equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 3 (1998): 585–629. http://dx.doi.org/10.1017/s030821050002165x.

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The existence of bright and dark multi-bump solitary waves for Ginzburg–Landau type perturbations of the cubic-quintic Schrodinger equation is considered. The waves in question are not perturbations of known analytic solitary waves, but instead arise as a bifurcation from a heteroclinic cycle in a three-dimensional ODE phase space. Using geometric singular perturbation techniques, regions in parameter space for which 1-bump bright and dark solitary waves will bifurcate are identified. The existence of N-bump dark solitary waves (N ≧ 1) is shown via an application of the Exchange Lemma with Exponentially Small Error. N-bump bright solitary waves are shown to exist as a consequence of the work of Kapitula and Maier-Paape.

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21

Costin, Rodica D. "Analytic linearization of nonlinear perturbations of Fuchsian systems." Nonlinearity 21, no. 9 (August 7, 2008): 2083–97. http://dx.doi.org/10.1088/0951-7715/21/9/010.

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22

Kaad, Jens, and Ryszard Nest. "Canonical holomorphic sections of determinant line bundles." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 746 (January 1, 2019): 67–116. http://dx.doi.org/10.1515/crelle-2015-0114.

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Abstract We investigate the analytic properties of torsion isomorphisms (determinants) of mapping cone triangles of Fredholm complexes. Our main tool is a generalization to Fredholm complexes of the perturbation isomorphisms constructed by R. Carey and J. Pincus for Fredholm operators. A perturbation isomorphism is a canonical isomorphism of determinants of homology groups associated to a finite rank perturbation of Fredholm complexes. The perturbation isomorphisms allow us to establish the invariance properties of the torsion isomorphisms under finite rank perturbations. We then show that the perturbation isomorphisms provide a holomorphic structure on the determinant lines over the space of Fredholm complexes. Finally, we establish that the torsion isomorphisms and the perturbation isomorphisms provide holomorphic sections of certain determinant line bundles.

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23

BARTUCCELLI, MICHELE, and GUIDO GENTILE. "LINDSTEDT SERIES FOR PERTURBATIONS OF ISOCHRONOUS SYSTEMS: A REVIEW OF THE GENERAL THEORY." Reviews in Mathematical Physics 14, no. 02 (February 2002): 121–71. http://dx.doi.org/10.1142/s0129055x02001120.

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We give a proof of the persistence of invariant tori for analytic perturbations of isochronous systems by using the Lindstedt series expansion for the solutions of the equations of motion. With respect to the case of anisochronous systems, there is the additional problem of finding the set of allowed rotation vectors, because they cannot be given a priori simply by looking at the unperturbed system. By considering the involved parameters (size of the perturbation, rotation vector and average action of a persisting invariant torus) as independent parameters we can introduce a function which is analytic in such parameters and only when the latter satisfy some constraint it becomes a solution: this can be regarded as a sort of singular implicit function problem. Therefore, although the dependence of the parameters, hence of the solution, upon the size of the perturbation is not smooth, in this way we construct explicitly the solution by using an absolutely convergent power series.

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24

Zimdahl, W., H. E. S. Velten, and W. C. Algoner. "Matter growth in extended ΛCDM cosmology." International Journal of Modern Physics D 28, no. 06 (April 2019): 1950086. http://dx.doi.org/10.1142/s021827181950086x.

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On the basis of a previously established scalar–tensor extension of the [Formula: see text]CDM model, we develop an effective fluid approach for the matter growth function. This extended [Formula: see text]CDM (henceforth [Formula: see text]CDM) cosmology takes into account deviations from the Standard Model both via a modified background expansion and by the inclusion of geometric anisotropic stresses as well as of perturbations of the geometric dark-energy equivalent. The background dynamics is governed by an explicit analytic expression for the Hubble rate in which modifications of the Standard Model are given in terms of a single constant parameter [W. C. Algoner, H. E. S. Velten and W. Zimdahl, J. Cosmol. Astropart. Phys. 1611 (2016) 034]. To close the system of fluid-dynamical perturbation equations, we introduce two phenomenological parameters through which the anisotropic stress is related both to the total energy density perturbation of the cosmic substratum and to relative perturbations in the effective two-component system. We quantify the impact of deviations from the standard background, of anisotropic stresses and of nonvanishing perturbations of the effective dark-energy component on the matter growth rate function [Formula: see text] and confront the results with recent redshift-space distortion (RSD) measurements.

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25

Gilliam, D. S., T. Hohage, X. Ji, and F. Ruymgaart. "The Fréchet Derivative of an Analytic Function of a Bounded Operator with Some Applications." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–17. http://dx.doi.org/10.1155/2009/239025.

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The main result in this paper is the determination of the Fréchet derivative of an analytic function of a bounded operator, tangentially to the space of all bounded operators. Some applied problems from statistics and numerical analysis are included as a motivation for this study. The perturbation operator (increment) is not of any special form and is not supposed to commute with the operator at which the derivative is evaluated. This generality is important for the applications. In the Hermitian case, moreover, some results on perturbation of an isolated eigenvalue, its eigenprojection, and its eigenvector if the eigenvalue is simple, are also included. Although these results are known in principle, they are not in general formulated in terms of arbitrary perturbations as required for the applications. Moreover, these results are presented as corollaries to the main theorem, so that this paper also provides a short, essentially self-contained review of these aspects of perturbation theory.

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26

CZINNER, VIKTOR, MÁTYÁS VASÚTH, and ÁRPÁD LUKÁCS. "AN ANALYTIC APPROACH TO THE LATE ISW EFFECT IN A Λ DOMINATED UNIVERSE." International Journal of Modern Physics A 20, no. 30 (December 10, 2005): 7233–40. http://dx.doi.org/10.1142/s0217751x05024328.

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The integrated Sachs–Wolfe (ISW) effect in a Λ dominated universe can be an important factor in the evolution of cosmic microwave background fluctuations. With the inclusion of cosmological constant we present the complete analytic solution of the covariant linear perturbations of the Einstein equations in the Newtonian gauge, in the case of a spatially flat (K = 0), Friedman–Robertson–Walker (FRW) universe, filled with pressureless ideal fluid. We use the analytic time dependence of the perturbation potentials to derive the anisotropy power spectrum of the late ISW effect. We choose the scale invariant Harrison–Zeldovich spectrum for obtaining the Cℓ momenta and show the agreement of our results with earlier, numeric calculations.

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27

KODAMA, HIDEO, and MISAO SASAKI. "EVOLUTION OF ISOCURVATURE PERTURBATIONS II: RADIATION-DUST UNIVERSE." International Journal of Modern Physics A 02, no. 02 (April 1987): 491–560. http://dx.doi.org/10.1142/s0217751x8700020x.

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Density perturbations in a universe in which matter consists of noninteracting nonrelativistic particles(dust) and strongly coupled photon-baryon fluid(radiation) are analyzed in terms of the gauge-invariant formalism extended to a multi-component system. Detailed analytic estimate is presented for the time evolution of both primordially adiabatic and primordially isocurvature perturbations. In particular, analytic formulas for characteristic scales appearing in the transfer functions are derived. The evolutionary behavior of these two types of perturbations are compared and the origins of their differences and similarities are clarified.

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28

GENTILE, GUIDO, MICHELE V. BARTUCCELLI, and JONATHAN H. B. DEANE. "BIFURCATION CURVES OF SUBHARMONIC SOLUTIONS AND MELNIKOV THEORY UNDER DEGENERACIES." Reviews in Mathematical Physics 19, no. 03 (April 2007): 307–48. http://dx.doi.org/10.1142/s0129055x07002985.

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We study perturbations of a class of analytic two-dimensional autonomous systems with perturbations depending periodically on time; for instance one can imagine a periodically driven or forced system with one degree of freedom. In the first part of the paper, we revisit a problem considered by Chow and Hale on the existence of subharmonic solutions. In the analytic setting, under more general (weaker) conditions on the perturbation, we prove their results on the bifurcation curves dividing the region of non-existence from the region of existence of subharmonic solutions. In particular our results apply also when one has degeneracy to the first order — i.e. when the subharmonic Melnikov function is identically constant. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalizations to higher orders of the subharmonic Melnikov function are also identically constant. The bifurcation curves consist of four branches joining continuously at the origin, where each of them can have a singularity (although generically they do not). The branches can form a cusp at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The method we use is completely different from that of Chow and Hale, and it is essentially based on the proof of convergence of the perturbation theory. It also allows us to treat the Melnikov theory in degenerate cases in which the subharmonic Melnikov function is either identically vanishing or has a zero which is not simple. This is investigated at length in the second part of the paper. When the subharmonic Melnikov function has a non-simple zero, we consider explicitly the case where there exist subharmonic solutions, which, although not analytic, still admit a convergent fractional series in the perturbation parameter.

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29

Fontich, Ernest, and Pau Martín. "Arnold diffusion in perturbations of analytic integrable Hamiltonian systems." Discrete & Continuous Dynamical Systems - A 7, no. 1 (2001): 61–84. http://dx.doi.org/10.3934/dcds.2001.7.61.

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30

Dubovik, Sergey A. "Analytic Designing of Regulators for System with Singular Perturbations." Journal of Automation and Information Sciences 31, no. 11 (1999): 40–52. http://dx.doi.org/10.1615/jautomatinfscien.v31.i11.70.

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31

Besova, Margarita, and Vasiliy Kachalov. "Axiomatic Approach in the Analytic Theory of Singular Perturbations." Axioms 9, no. 1 (January 16, 2020): 9. http://dx.doi.org/10.3390/axioms9010009.

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Introduced by S.A. Lomov, the concept of a pseudoanalytic (pseudoholomorphic) solution laid the foundation for the development of the singular perturbation analytical theory. In order for this concept to work in case of linear problems, an apparatus for the theory of exponential type vector spaces was developed. When considering nonlinear singularly perturbed problems, an algebraic approach is currently used. This approval is based on the properties of algebra homomorphisms for holomorphic functions with various numbers of variables, as a result of which it is possible to obtain pseudoholomorphic solutions. In this paper, formally singularly perturbed equations are considered in topological algebras, which allows the authors to formulate the main concepts of the singular perturbation analytical theory from the standpoint of maximal generality.

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32

Fontich, Ernest, and Pau Martı́n. "Arnold diffusion in perturbations of analytic exact symplectic maps." Nonlinear Analysis: Theory, Methods & Applications 42, no. 8 (December 2000): 1397–412. http://dx.doi.org/10.1016/s0362-546x(99)00160-1.

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33

Lau, Stephen R. "Analytic structure of radiation boundary kernels for blackhole perturbations." Journal of Mathematical Physics 46, no. 10 (October 2005): 102503. http://dx.doi.org/10.1063/1.2073287.

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34

Thilliez, Vincent. "On the stability of analytic germs under ultradifferentiable perturbations." Journal of Mathematical Analysis and Applications 328, no. 2 (April 2007): 1141–51. http://dx.doi.org/10.1016/j.jmaa.2006.06.009.

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35

Sarris, T., X. Li, and M. Temerin. "Simulating radial diffusion of energetic (MeV) electrons through a model of fluctuating electric and magnetic fields." Annales Geophysicae 24, no. 10 (October 20, 2006): 2583–98. http://dx.doi.org/10.5194/angeo-24-2583-2006.

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Abstract. In the present work, a test particle simulation is performed in a model of analytic Ultra Low Frequency, ULF, perturbations in the electric and magnetic fields of the Earth's magnetosphere. The goal of this work is to examine if the radial transport of energetic particles in quiet-time ULF magnetospheric perturbations of various azimuthal mode numbers can be described as a diffusive process and be approximated by theoretically derived radial diffusion coefficients. In the model realistic compressional electromagnetic field perturbations are constructed by a superposition of a large number of propagating electric and consistent magnetic pulses. The diffusion rates of the electrons under the effect of the fluctuating fields are calculated numerically through the test-particle simulation as a function of the radial coordinate L in a dipolar magnetosphere; these calculations are then compared to the symmetric, electromagnetic radial diffusion coefficients for compressional, poloidal perturbations in the Earth's magnetosphere. In the model the amplitude of the perturbation fields can be adjusted to represent realistic states of magnetospheric activity. Similarly, the azimuthal modulation of the fields can be adjusted to represent different azimuthal modes of fluctuations and the contribution to radial diffusion from each mode can be quantified. Two simulations of quiet-time magnetospheric variability are performed: in the first simulation, diffusion due to poloidal perturbations of mode number m=1 is calculated; in the second, the diffusion rates from multiple-mode (m=0 to m=8) perturbations are calculated. The numerical calculations of the diffusion coefficients derived from the particle orbits are found to agree with the corresponding theoretical estimates of the diffusion coefficient within a factor of two.

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36

BARREIRA, LUIS, and CLAUDIA VALLS. "Asymptotic behavior of distribution of frequencies of digits." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 1 (July 2008): 177–95. http://dx.doi.org/10.1017/s0305004108001254.

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AbstractWe present an approach to compute the Hausdorff dimension of a class of sets of real numbers that are defined in terms of nonlinear relations between frequencies of digits in some integer base m. We consider the model case of quadratic perturbations, for which the computations are already rather involved. We show that the Hausdorff dimension is analytic in the parameter determining the perturbation. Our approach also allows to estimate the asymptotic behavior of the Taylor coefficients of the dimension in terms of m.

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37

Gong, Jinn-Ouk. "Analytic Integral Solutions for Induced Gravitational Waves." Astrophysical Journal 925, no. 1 (January 1, 2022): 102. http://dx.doi.org/10.3847/1538-4357/ac3a6c.

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Abstract We present analytic integral solutions for the second-order induced gravitational waves (GWs). After presenting all the possible second-order source terms, we calculate explicitly the solutions for the GWs induced by the linear scalar and tensor perturbations during matter- and radiation-dominated epochs.

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38

Monti, F., and H. R. Jauslin. "Quantum Nekhoroshev Theorem for Quasi-Periodic Floquet Hamiltonians." Reviews in Mathematical Physics 10, no. 03 (April 1998): 393–428. http://dx.doi.org/10.1142/s0129055x98000124.

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A quantum version of Nekhoroshev estimates for Floquet Hamiltonians associated to quasi-periodic time dependent perturbations is developped. If the unperturbed energy operator has a discrete spectrum and under finite Diophantine conditions, an effective Floquet Hamiltonian with pure point spectrum is constructed. For analytic perturbations, the effective time evolution remains close to the original Floquet evolution up to exponentially long times. We also treat the case of differentiable perturbations.

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39

LIU, TAO, LIANGGANG WU, and FENG LI. "ANALYTIC CENTER OF NILPOTENT CRITICAL POINTS." International Journal of Bifurcation and Chaos 22, no. 08 (August 2012): 1250198. http://dx.doi.org/10.1142/s0218127412501982.

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For third-order nilpotent critical points of a planar dynamical system, the analytic center problem is completely solved in this article by using the integrating factor method. The associated quasi-Lyapunov constants are defined and their computation method is given. For a class of cubic-order systems under small perturbations, sufficient and necessary conditions for an analytic center are obtained.

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40

Wolfson, Ira. "Analytic correlation of inflationary potential to power spectrum shape: limits of validity, and `no-go' for small field model analytics." Journal of Cosmology and Astroparticle Physics 2022, no. 01 (January 1, 2022): 036. http://dx.doi.org/10.1088/1475-7516/2022/01/036.

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Abstract The primordial power spectrum informs the possible inflationary histories of our universe. Given a power spectrum, the ensuing cosmic microwave background is calculated and compared to the observed one. Thus, one focus of modern cosmology is building well-motivated inflationary models that predict the primordial power spectrum observables. The common practice uses analytic terms for the scalar spectral index ns and the index running α, forgoing the effort required to evaluate the model numerically. However, the validity of these terms has never been rigorously probed and relies on perturbative methods, which may lose their efficacy for large perturbations. The requirement for more accurate theoretical predictions becomes crucial with the advent of highly sensitive measuring instruments. This paper probes the limits of the perturbative treatment that connects inflationary potential parameters to primordial power spectrum observables. We show that the validity of analytic approximations of the scalar index roughly respects the large-field/small-field dichotomy. We supply an easily calculated measure for relative perturbation amplitude and show that, for large field models, the validity of analytical terms extends to ∼ 3% perturbation relative to a power-law inflation model. Conversely, the analytical treatment loses its validity for small field models with as little as 0.1% perturbation relative to the small-field test-case. By employing the most general artificial neural networks and multinomial functions up to the twentieth degree and demonstrating their shortcomings, we show that no reasonable and universal analytic expressions correlating small field models to the observables they yield exists. Finally, we discuss the possible implications of this work and supply the validity heuristic for large and small field models.

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Sende, J. A., and T. Löhne. "Twisted debris: how differential secular perturbations shape debris disks." Astronomy & Astrophysics 631 (November 2019): A141. http://dx.doi.org/10.1051/0004-6361/201935199.

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Context. Resolved images suggest that asymmetric structures are a common feature of cold debris disks. While planets close to these disks are rarely detected, their hidden presence and gravitational perturbations provide plausible explanations for some of these features. Aims. To put constraints on the properties of yet undetected planetary companions, we aim to predict what features such a planet imprints in debris disks undergoing continuous collisional evolution. Methods. We discuss the basic equations, analytic approximations and timescales governing collisions, radiation pressure and secular perturbations. In addition, we combine our numerical model of the collisional evolution of the size and spatial distributions in debris disks with the gravitational perturbation by a single planet. Results. We find that the distributions of orbital elements in the disks are strongly dependent on grain sizes. Secular precession is differential with respect to involved semi-major axes and grain sizes. This leads to observable differences between the big grains tracing the parent belt and the small grains in the trailing halo. Observations at different wavelengths can be used to constrain the properties of a possible planet.

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Chen, Qinbo, and Rafael de la Llave. "Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems." Nonlinearity 35, no. 4 (March 9, 2022): 1986–2019. http://dx.doi.org/10.1088/1361-6544/ac50bb.

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Abstract The genericity of Arnold diffusion in the analytic category is an open problem. In this paper, we study this problem in the following a priori unstable Hamiltonian system with a time-periodic perturbation H ε ( p , q , I , φ , t ) = h ( I ) + ∑ i = 1 n ± 1 2 p i 2 + V i ( q i ) + ε H 1 ( p , q , I , φ , t ) , where ( p , q ) ∈ R n × T n , ( I , φ ) ∈ R d × T d with n, d ⩾ 1, V i are Morse potentials, and ɛ is a small non-zero parameter. The unperturbed Hamiltonian is not necessarily convex, and the induced inner dynamics does not need to satisfy a twist condition. Using geometric methods we prove that Arnold diffusion occurs for generic analytic perturbations H 1. Indeed, the set of admissible H 1 is C ω dense and C 3 open (a fortiori, C ω open). Our perturbative technique for the genericity is valid in the C k topology for all k ∈ [3, ∞) ∪ {∞, ω}.

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Mazzocco, M. "KAM theorem for generic analytic perturbations of the Euler system." Zeitschrift für angewandte Mathematik und Physik 48, no. 2 (March 1997): 193–219. http://dx.doi.org/10.1007/pl00001474.

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Demers, Mark F., and Hong-Kun Zhang. "A Functional Analytic Approach to Perturbations of the Lorentz Gas." Communications in Mathematical Physics 324, no. 3 (October 17, 2013): 767–830. http://dx.doi.org/10.1007/s00220-013-1820-0.

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Kim, Hyeong-Chan, and Masato Minamitsuji. "An analytic approach to perturbations from an initially anisotropic universe." Journal of Cosmology and Astroparticle Physics 2011, no. 03 (March 23, 2011): 038. http://dx.doi.org/10.1088/1475-7516/2011/03/038.

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Gaidashev, Denis. "On analytic perturbations of a family of Feigenbaum-like equations." Journal of Mathematical Analysis and Applications 374, no. 2 (February 2011): 355–73. http://dx.doi.org/10.1016/j.jmaa.2010.06.047.

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Berriochoa, E., A. Cachafeiro, and F. Marcellán. "Szegő transformation and zeros of analytic perturbations of Chebyshev weights." Journal of Mathematical Analysis and Applications 470, no. 1 (February 2019): 571–83. http://dx.doi.org/10.1016/j.jmaa.2018.10.021.

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BIRMINGHAM, DANNY. "CHOPTUIK SCALING AND QUASINORMAL MODES IN THE ADS/CFT CORRESPONDENCE." International Journal of Modern Physics A 17, no. 20 (August 10, 2002): 2750. http://dx.doi.org/10.1142/s0217751x02011771.

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The exact quasinormal frequencies for scalar perturbations of the three-dimensional BTZ black hole were presented1. The timescale for the decay of the scalar perturbation is given by the imaginary part of the quasinormal frequencies. Via the AdS/CFT correspondence, one then obtains a prediction of the timescale for return to equilibrium of the dual conformal field theory. By studying a two-particle collision process, an exact analytic expression for the Choptuik scaling parameter of the BTZ black hole was obtained2. A possible connection between the Choptuik scaling parameter and the imaginary part of the quasinormal frequencies was explored1.

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Zhou, Huan, Wei Zheng, and Guojian Tang. "Ballistic error propagation algorithm for glide trajectory based on perturbation theory." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 9 (July 7, 2016): 1574–92. http://dx.doi.org/10.1177/0954410016656874.

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A ballistic error propagation algorithm for glide trajectories of a hypersonic glide vehicle is originally proposed based on the perturbation theory. Perturbation equations that treat perturbations as external inputs and flight state deviations as state variables are established. Based on the reasonable simplification assumptions, the analytic expression of the state transition matrix is deduced and thus the ballistic error propagation model is established. A transposed coordinate frame is introduced to simplify the development of the perturbation equations and the error propagation model. By employing the gravity anomaly as the single perturbation factor, the proposed algorithm is validated and verified by numerical experiments. When compared with the traditional method, the proposed method takes only just a quarter computational costs and restrains the method errors beneath 10% of the total terminal deviations. It is an effort that initially focuses on the error propagation mechanism of the glide trajectory and the proposed model has sufficient precision for the analysis of modeling deviations, thus laying the foundation of correcting the modeling deviations and enhancing the accuracy of vehicle’s flight states.

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Yoder, C. F., and E. R. Ivins. "Improved Analytic Nutation Model." Symposium - International Astronomical Union 129 (1988): 379–80. http://dx.doi.org/10.1017/s0074180900135077.

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Models describing earth's nutations can be separated into two major components, plus several small perturbations, of which ocean tides and solid friction are the most significant. The primary element of a successful model is an accurate rigid earth nutation theory. The effect of mantle elasticity and differential nutation of the fluid core is then obtained as a correction factor which multiplies the rigid body result. Wahr's (1981) theory is certainly the most sophisticated elastodynamic response model. However, we have found that the simple model of Sasao et al., (1980) differs from Wahr's theory term by term by less than 0.3mas if a modern earth structure model (1066B) is used to evaluate the nutation structure constants.

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