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Добірка наукової літератури з теми "Partially Hyperbolic System"

Автор: Grafiati

Опубліковано: 11 березня 2023

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Статті в журналах з теми "Partially Hyperbolic System"

1

RIOS, I., and J. SIQUEIRA. "On equilibrium states for partially hyperbolic horseshoes." Ergodic Theory and Dynamical Systems 38, no. 1 (2016): 301–35. http://dx.doi.org/10.1017/etds.2016.21.

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We prove the existence and uniqueness of equilibrium states for a family of partially hyperbolic systems, with respect to Hölder continuous potentials with small variation. The family comes from the projection, on the center-unstable direction, of a family of partially hyperbolic horseshoes introduced by Díaz et al [Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes. Ergod. Th. & Dynam. Sys.29 (2009), 433–474]. For the original three-dimensional system we consider potentials with small variation, constant on local stable manifolds, obtaining existence and uniqueness of equilibrium states.

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2

RODRIGUEZ HERTZ, F., M. A. RODRIGUEZ HERTZ, A. TAHZIBI, and R. URES. "Maximizing measures for partially hyperbolic systems with compact center leaves." Ergodic Theory and Dynamical Systems 32, no. 2 (2011): 825–39. http://dx.doi.org/10.1017/s0143385711000757.

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AbstractWe obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy, we obtain that the system is topologically conjugated to a rotation extension of a hyperbolic system. This implies that the second case of the dichotomy holds for an open and dense set of diffeomorphisms in the hypothesis of our result. As a consequence, we obtain an open set of topologically mixing diffeomorphisms having more than one entropy-maximizing measure.

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3

ANDERSSON, MARTIN, and CARLOS H. VÁSQUEZ. "On mostly expanding diffeomorphisms." Ergodic Theory and Dynamical Systems 38, no. 8 (2017): 2838–59. http://dx.doi.org/10.1017/etds.2017.17.

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In this work, we study the class of mostly expanding partially hyperbolic diffeomorphisms. We prove that such a class is$C^{r}$-open,$r>1$, among the partially hyperbolic diffeomorphisms and we prove that the mostly expanding condition guarantees the existence of physical measures and provides more information about the statistics of the system. Mañé’s classical derived-from-Anosov diffeomorphism on$\mathbb{T}^{3}$belongs to this set.

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4

Xu, Jiang, and Shuichi Kawashima. "Global Classical Solutions for Partially Dissipative Hyperbolic System of Balance Laws." Archive for Rational Mechanics and Analysis 211, no. 2 (2013): 513–53. http://dx.doi.org/10.1007/s00205-013-0679-8.

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5

BUZZI, J., T. FISHER, M. SAMBARINO, and C. VÁSQUEZ. "Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems." Ergodic Theory and Dynamical Systems 32, no. 1 (2011): 63–79. http://dx.doi.org/10.1017/s0143385710000854.

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AbstractWe show that a class of robustly transitive diffeomorphisms originally described by Mañé are intrinsically ergodic. More precisely, we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic and structurally stable, but nevertheless have the following stability with respect to their entropy. Their topological entropy is constant and they each have a unique measure of maximal entropy with respect to which periodic orbits are equidistributed. Moreover, equipped with their respective measure of maximal entropy, these diffeomorphisms are pairwise isomorphic. We show that the method applies to several classes of systems which are similarly derived from Anosov, i.e. produced by an isotopy from an Anosov system, namely, a mixed Mañé example and one obtained through a Hopf bifurcation.

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6

Ondich, Jeffrey. "The reducibility of partially invariant solutions of systems of partial differential equations." European Journal of Applied Mathematics 6, no. 4 (1995): 329–54. http://dx.doi.org/10.1017/s0956792500001881.

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Ovsiannikov's partially invariant solutions of differential equations generalize Lie's group invariant solutions. A partially invariant solution is only interesting if it cannot be discovered more readily as an invariant solution. Roughly, a partially invariant solution that can be discovered more directly by Lie's method is said to be reducible. In this paper, I develop conditions under which a partially invariant solution or a class of such solutions must be reducible, and use these conditions both to obtain non-reducible solutions to a system of hyperbolic conservation laws, and to demonstrate that some systems have no non-reducible solutions. I also demonstrate that certain elliptic systems have no non-reducible solutions.

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7

Vergara-Hermosilla, G., G. Leugering, and Y. Wang. "Boundary controllability of a system modelling a partially immersed obstacle." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 80. http://dx.doi.org/10.1051/cocv/2021076.

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In this paper, we address the problem of boundary controllability for the one-dimensional nonlinear shallow water system, describing the free surface flow of water as well as the flow under a fixed gate structure. The system of differential equations considered can be interpreted as a simplified model of a particular type of wave energy device converter called oscillating water column. The physical requirements naturally lead to the problem of exact controllability in a prescribed region. In particular, we use the concept of nodal profile controllability in which at a given point (the node) time-dependent profiles for the states are required to be reachable by boundary controls. By rewriting the system into a hyperbolic system with nonlocal boundary conditions, we at first establish the semi-global classical solutions of the system, then get the local controllability and nodal profile using a constructive method. In addition, based on this constructive process, we provide an algorithmic concept to calculate the required boundary control function for generating a solution for solving these control problem.

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8

Klar, A., and O. Tse. "An entropy functional and explicit decay rates for a nonlinear partially dissipative hyperbolic system." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 95, no. 5 (2014): 469–75. http://dx.doi.org/10.1002/zamm.201300275.

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9

GUPTA, CHINMAYA. "Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems." Ergodic Theory and Dynamical Systems 30, no. 3 (2009): 757–71. http://dx.doi.org/10.1017/s0143385709000406.

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AbstractIn this note, we obtain verifiable sufficient conditions for the extreme-value distribution for a certain class of skew-product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the decay of correlations on the product system and the measure of rapidly returning points on the base, lead to a distribution for the maximum of Φ(p)=−log(d(p,p0)) that is of the first type. In particular, we establish the type I distribution for S1 extensions of piecewise C2 uniformly expanding maps of the interval, non-uniformly expanding maps of the interval modeled by a Young tower, and a skew-product extension of a uniformly expanding map with a curve of neutral points.

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10

Rempel, M., and D. Przybylski. "Efficient Numerical Treatment of Ambipolar and Hall Drift as Hyperbolic System." Astrophysical Journal 923, no. 1 (2021): 79. http://dx.doi.org/10.3847/1538-4357/ac2c6d.

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Abstract Partially ionized plasmas, such as the solar chromosphere, require a generalized Ohm’s law including the effects of ambipolar and Hall drift. While both describe transport processes that arise from the multifluid equations and are therefore of hyperbolic nature, they are often incorporated in models as a diffusive, i.e., parabolic process. While the formulation as such is easy to include in standard MHD models, the resulting diffusive time-step constraints do require often a computationally more expensive implicit treatment or super-time-stepping approaches. In this paper we discuss an implementation that retains the hyperbolic nature and allows for an explicit integration with small computational overhead. In the case of ambipolar drift, this formulation arises naturally by simply retaining a time derivative of the drift velocity that is typically omitted. This alone leads to time-step constraints that are comparable to the native MHD time-step constraint for a solar setup including the region from photosphere to lower solar corona. We discuss an accelerated treatment that can further reduce time-step constraints if necessary. In the case of Hall drift we propose a hyperbolic formulation that is numerically similar to that for the ambipolar drift and we show that the combination of both can be applied to simulations of the solar chromosphere at minimal computational expense.

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