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Relevant bibliographies by topics / Restricted orbit equivalence

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Academic literature on the topic 'Restricted orbit equivalence'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 February 2022

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Journal articles on the topic "Restricted orbit equivalence"

1

Rudolph, Daniel J. "Restricted orbit equivalence." Memoirs of the American Mathematical Society 54, no. 323 (1985): 0. http://dx.doi.org/10.1090/memo/0323.

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KAMMEYER, JANET WHALEN, and DANIEL J. RUDOLPH. "Restricted orbit equivalence for ergodic ${\Bbb Z}^{d}$ actions I." Ergodic Theory and Dynamical Systems 17, no. 5 (October 1997): 1083–129. http://dx.doi.org/10.1017/s0143385797086288.

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In [R1] a notion of restricted orbit equivalence for ergodic transformations was developed. Here we modify that structure in order to generalize it to actions of higher-dimensional groups, in particular ${\Bbb Z}^d$-actions. The concept of a ‘size’ is developed first from an axiomatized notion of the size of a permutation of a finite block in ${\Bbb Z}^d$. This is extended to orbit equivalences which are cohomologous to the identity and, via the natural completion, to a notion of restricted orbit equivalence. This is shown to be an equivalence relation. Associated to each size is an entropy which is an equivalence invariant. As in the one-dimensional case this entropy is either the classical entropy or is zero. Several examples are discussed.

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3

Fieldsteel, Adam, and N. A. Friedman. "Restricted orbit changes of ergodic ℤd-actions to achieve mixing and completely positive entropy." Ergodic Theory and Dynamical Systems 6, no. 4 (December 1986): 505–28. http://dx.doi.org/10.1017/s0143385700003667.

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AbstractWe show that for every ergodic ℤd-action T, there is a mixing ℤd-action S which is orbit equivalent to T via an orbit equivalence that is a weak a-equivalence for all a ≥ 1 and a strong b-equivalence for all b ∈ (0, 1). If T has positive entropy, then S can be taken to have completely positive entropy. If the dimension d is greater than one, the orbit equivalence may be taken to be bounded and a strong b-equivalence for all b > 0.

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MORTISS, GENEVIEVE. "A non-singular inverse Vitali lemma with applications." Ergodic Theory and Dynamical Systems 20, no. 4 (August 2000): 1215–29. http://dx.doi.org/10.1017/s0143385700000651.

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A proof for a non-singular version of the inverse Vitali lemma is given. The result is used to describe non-singular orbit equivalence within the framework of Rudolph's restricted orbit equivalence and in the construction of an alternative proof of the Hurewicz ergodic theorem.

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ŞAHIN, AYŞE ARZU. "Tiling representations of ${\Bbb R}^{\bf 2}$ actions and $\balpha$-equivalence in two dimensions." Ergodic Theory and Dynamical Systems 18, no. 5 (October 1998): 1211–55. http://dx.doi.org/10.1017/s0143385798117522.

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We study ${\Bbb Z}^2$ actions arising as base point actions of tiling representations of ${\Bbb R}^2$ flows. We cast an equivalence relation between such actions in terms of a simple arithmetic condition on an orbit equivalence. Stated as such, our equivalence class is easily seen to be a restricted even Kakutani equivalence, as we well as a higher-dimensional generalization of $\alpha$-equivalence, defined by Fieldsteel, del Junco and Rudolph for ${\Bbb Z}$ actions.

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6

Hinrichsen, D., and J. O’Halloran. "A Complete Characterization of Orbit Closures of Controllable Singular Systems under Restricted System Equivalence." SIAM Journal on Control and Optimization 28, no. 3 (March 1990): 602–23. http://dx.doi.org/10.1137/0328036.

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Fieldsteel, Adam, Andrés Del Junco, and Daniel J. Rudolph. "α-equivalence: a refinement of Kakutani equivalence." Ergodic Theory and Dynamical Systems 14, no. 1 (March 1994): 69–102. http://dx.doi.org/10.1017/s0143385700007732.

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AbstractFor a fixed irrational α > 0 we say that probability measure-preserving transformationsSandTare α-equivalent if they can be realized as cross-sections in a common flow such that the return time functions on the cross-sections both take values in {1, 1 +α} and have equal integrals. Similarly we call two flowsFandGα-equivalent ifFhas a cross-sectionSandGhas a cross-sectionTisomorphic toSand again both the return time functions take values in {1, 1 + α} and have equal integrals. The integer kα(S), equal to the least positivesuchsuch that exp2πikα-1belongs to the point spectrum ofS, is an invariant of α-equivalence.We obtain a characterization of a-equivalence as a particular type of restricted orbit equivalence and use this to prove that within the class of loosely Bernoulli mapska(S) together with the entropyh(S) are complete invariants of α-equivalence. There is a corresponding a-equivalence theorem for flows which has as a consequence, for example, that up to an obvious entropy restriction, any weakly mixing cross-section of a loosely Bernoulli flow can also be realized as a cross-section with a {1,1 + α}-valued return time function.For the proof of the α-equivalence theorem we develop a relative Kakutani equivalence theorem for compact group extensions which is of interest in its own right. Finally, an example of Fieldsteel and Rudolph is used to show that in generalkα(S) is not a complete invariant of α-equivalence within a given even Kakutani equivalence class.

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Clotet, Josep, and M. Dolors Magret. "Dimension of orbits of linear time-invariant singular systems under restricted system equivalence." Linear Algebra and its Applications 429, no. 5-6 (September 2008): 1102–13. http://dx.doi.org/10.1016/j.laa.2007.05.018.

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9

Wex, Norbert. "Testing the Strong Equivalence Principle in strong field regimes." International Astronomical Union Colloquium 160 (1996): 123–24. http://dx.doi.org/10.1017/s0252921100041221.

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A possible functional dependence of the ratio of ‘gravitational’ massmGand ‘inertial’ massmIon the gravitational self-energyEG,is called aviolation of the Strong Equivalence Principle (SEP).Weakly self-gravitating bodies are found in the solar system where lunarlaser-ranging data restrict the Nordtvedt parameter η to absolute values smaller than 0.001, (Dickey et al. 1994, Müller et al. 1995). To test higher order contributions one needs to consider strongly self-gravitating bodies such as neutron-stars.Small-eccentricity binary-star systems consisting of a neutron star (|EG|/mc2~ 0.15) and a white dwarf (|EG|/mc2~ 10−4) are excellent ‘laboratories’ to test the SEP in a strong-field regime. As shown by Damour and Schäfer (1991) a violation of the SEP would lead to a periodic change in the eccentricity of the orbit of the binary pulsar caused by the galactic acceleration. Thus the observation of old small-eccentricity long-orbital-period neutron-star white-dwarf binary systems put (with a certain confidence level) a limit on the violation of the SEP.

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Wang, Yue, and Xiaojie Wu. "Analysis of Phobos’ dynamical environment considering effects of ephemerides and physical libration." Monthly Notices of the Royal Astronomical Society 497, no. 1 (July 10, 2020): 416–34. http://dx.doi.org/10.1093/mnras/staa1948.

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ABSTRACT A dynamical model is developed in the body-fixed frame of Phobos, in which the high-precision gravity field and exact physical libration of Phobos, the gravity of Mars with J2, and the gravity perturbations of the Sun, Jupiter, and Earth are considered. The JPL development ephemeris are applied to calculate the positions of celestial bodies. Phobos is considered as a homogeneous polyhedron with 16 037 vertices to characterize its irregular shape and the corresponding gravity field. The physical libration of Phobos is incorporated into its rotational motion by using the results in ‘Report of the IAU WGCCRE’. With the proposed model, equivalent gravity and slope on Phobos surface are calculated and analysed. The liftoff velocity is also computed and presented. Besides, the orbital environment is also investigated. Instantaneous equilibrium points in the Mars–Phobos system are computed and demonstrated, and the acceleration of a particle in the vicinity of Phobos is analysed to find out the main influencing factor in different regions. Quasi-satellite orbits and libration point orbits, which were determined in the circular restricted three-body problem model, are simulated in different dynamical models. The results applying the newly developed high-fidelity dynamical model have shown significant differences with respect to existing models, suggesting that dynamical models with higher accuracy are needed for close-range orbital activities.

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Dissertations / Theses on the topic "Restricted orbit equivalence"

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Mortiss, Genevieve Catherine Mathematics UNSW. "Average co-ordinate entropy and a non-singular version of restricted orbit equivalence." Awarded by:University of New South Wales. Mathematics, 1997. http://handle.unsw.edu.au/1959.4/17823.

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A notion of entropy is defined for the non-singular action of finite co-ordinate changes on X - the infinite product of two- point spaces. This quantity - average co-ordinate or AC entropy - is calculated for product measures and G-measures on X, and an equivalence relation is established for which AC entropy is an invariant. The Inverse Vitali Lemma is discussed in a measure preserving context, and it is shown that for a certain class of measures on X known as odometer bounded, the result will still hold for odometer actions. The foundations for a non-singular version of Rudolph's restricted orbit equivalence are established, and a size for non-singular orbit equivalence is introduced. It is shown that provided the Inverse Vitali Lemma still holds, the non-singular orbit equivalence classes can be described using this new size.

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Mortiss, Genevieve. "Average co-ordinate entropy and a non-singular version of restricted orbit equivalence." [Sydney : University of New South Wales], 1997. http://www.library.unsw.edu.au/~thesis/adt-NUN/public/adt-NUN1998.0001/index.html.

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Books on the topic "Restricted orbit equivalence"

1

Restricted orbit equivalence. Providence, R.I., USA: American Mathematical Society, 1985.

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2

Restricted Orbit Equivalence of Discrete Amenable Groups. Cambridge University Press, 2002.

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Book chapters on the topic "Restricted orbit equivalence"

1

"The Equivalence Theorem." In Restricted Orbit Equivalence for Actions of Discrete Amenable Groups, 139–66. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511549908.007.

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"Introduction." In Restricted Orbit Equivalence for Actions of Discrete Amenable Groups, 1–12. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511549908.001.

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3

"Definitions and Examples." In Restricted Orbit Equivalence for Actions of Discrete Amenable Groups, 13–48. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511549908.002.

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4

"The Ornstein–Weiss Machinery." In Restricted Orbit Equivalence for Actions of Discrete Amenable Groups, 49–64. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511549908.003.

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"Copying Lemmas." In Restricted Orbit Equivalence for Actions of Discrete Amenable Groups, 65–90. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511549908.004.

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6

"m-entropy." In Restricted Orbit Equivalence for Actions of Discrete Amenable Groups, 91–99. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511549908.005.

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7

"m-joinings." In Restricted Orbit Equivalence for Actions of Discrete Amenable Groups, 100–138. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511549908.006.

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8

"Bibliography." In Restricted Orbit Equivalence for Actions of Discrete Amenable Groups, 196–98. Cambridge University Press, 2002. http://dx.doi.org/10.1017/cbo9780511549908.009.

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Conference papers on the topic "Restricted orbit equivalence"

1

Torres Cedillo, Sergio G., and Philip Bonello. "Unbalance Identification and Balancing of Nonlinear Rotodynamic Systems." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-25290.

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This paper is devoted to the unbalance identification and balancing of an aircraft engine rotor running on Squeeze Film Damper (SFD) bearings that show highly nonlinear features. The high pressure (HP) rotor in a twin-spool assembly cannot be accessed under operational conditions because of the restricted space for instrumentation and temperatures that are beyond the safe operating limits of the sensors. This motivates the use of a non-invasive procedure, requiring prior knowledge of the structure. The only such method for rotating machinery with non-linear bearings reported in the literature is highly limited in its application (e.g. assumes circular centred orbits). The methodology proposed in this paper is aimed at overcoming such limitations. It uses the Receptance Harmonic Balance Method (RHBM) to generate the backward operator using vibration measurements taken from sensors installed on the engine casing. The operator is then inverted using either Least Squares Fit (LSF) or Singular Value Decomposition (SVD). The resulting solution is the equivalent unbalance distribution in prescribed unbalance planes of the HP rotor which are consequently used to balance it. This method is validated using two distinct rotordynamic systems and simulated casing vibration readings corrupted by different noise levels.

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