Escape from large holes in Anosov systems

2017 ◽  
pp. 29-38
Author(s):  
Valentin Afraimovich ◽  
Leonid Bunimovich
Keyword(s):  
Anosov Systems

Centralizers of derived-from-Anosov systems on : rigidity versus triviality

2021 ◽  
pp. 1-25
Author(s):  
SHAOBO GAN ◽  
YI SHI ◽  
DISHENG XU ◽  
JINHUA ZHANG
Keyword(s):  
Linear Part ◽  
Anosov Systems ◽  
Partially Hyperbolic ◽  
Partially Hyperbolic Diffeomorphism

Abstract In this paper, we study the centralizer of a partially hyperbolic diffeomorphism on ${\mathbb T}^3$ which is homotopic to an Anosov automorphism, and we show that either its centralizer is virtually trivial or such diffeomorphism is smoothly conjugate to its linear part.

Subsystems of Anosov Systems

1995 ◽  
Vol 117 (6) ◽  
pp. 1431 ◽  
Author(s):  
A. Zeghib
Keyword(s):  
Anosov Systems

Sur une notion d'autonomie de systèmes dynamiques, appliquée aux ensembles invariants des flots d' Anosov algébriques

1995 ◽  
Vol 15 (1) ◽  
pp. 175-207 ◽  
Author(s):  
A. Zeghib
Keyword(s):  
Dynamical Systems ◽  
Finite Volume ◽  
Algebraic Dynamical Systems ◽  
Anosov Systems ◽  
Anosov System ◽  
Autonomous Dynamical Systems

AbstractWe introduce a notion of autonomous dynamical systems which generalizes algebraic dynamical systems. We show by giving examples and by describing some properties that this generalization is not a trivial one. We apply the methods then developed to algebraic Anosov systems. We prove that a C1-submanifold of finite volume, which is invariant by an algebraic Anosov system is ‘essentially’ algebraic.

Maximal entropy measures for certain partially hyperbolic, derived from Anosov systems

2011 ◽  
Vol 32 (1) ◽  
pp. 63-79 ◽  
Author(s):  
J. BUZZI ◽  
T. FISHER ◽  
M. SAMBARINO ◽  
C. VÁSQUEZ
Keyword(s):  
Hopf Bifurcation ◽  
Maximal Entropy ◽  
Open Set ◽  
Entropy Measures ◽  
Unique Measure ◽  
Anosov Systems ◽  
Anosov System ◽  
Partially Hyperbolic ◽  
Structurally Stable ◽  
Measure Of Maximal Entropy

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.

scholarly journals Propriétés ergodiques, en mesure infinie, de certains systèmes dynamiques fibrés

1989 ◽  
Vol 9 (3) ◽  
pp. 433-453 ◽  
Author(s):  
Y. Guivarc'h
Keyword(s):  
Dynamical Systems ◽  
Invariant Measure ◽  
Geodesic Flow ◽  
Negative Curvature ◽  
Compact Manifolds ◽  
Constant Negative Curvature ◽  
Skew Products ◽  
Ergodic Properties ◽  
Anosov Systems

AbstractWe study the ergodic properties of a class of dynamical systems with infinite invariant measure. This class contains skew-products of Anosov systems with ℝd. The results are applied to theKproperty of skew-products and also to the ergodicity of the geodesic flow on abelian coverings of compact manifolds with constant negative curvature.

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