Symbolic dynamics for non-uniformly hyperbolic systems
نویسندگان
چکیده
منابع مشابه
Symbolic Dynamics for Hyperbolic Systems
◦ Geodesic flows on compact manifolds with negative sectional curvature. Later, we relax uniform hyperbolicity to an asymptotic one, called non-uniform hyperbolicity. Two examples of such systems are: ◦ Slow down of fA : T → T, see [9]. ◦ Geodesic flows on surfaces with nonpositive curvature. Introductory example: Smale’s horseshoe [21]. Let g : K → K be Smale’s horseshoe map, and σ : Σ→ Σ the ...
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Given an orbit whose linearization has invariant subspaces satisfying some non-resonance conditions in the exponential rates of growth, we prove existence of invariant manifolds tangent to these subspaces. The exponential rates of growth can be understood either in the sense of Lyapunov exponents or in the sense of exponential dichotomies. These manifolds can correspond to “slow manifolds”, whi...
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We consider an Axiom A diffeomorphism or a Markov map of an interval and the invariant set Ω∗ of orbits which never falls into a fixed hole. We study various aspects of the symbolic representation of Ω∗ and of its nonwandering set Ω. Our results are on the cardinality of the set of topologically transitive components of Ω and their structure. We also prove that Ω∗ is generically a subshift of f...
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We give a new proof of the fact that the eigenvalues at correspondig periodic orbits form a complete set of invariants for the smooth conjugacy of low dimensional Anosov systems. We also show that, if a homeomorphism conjugating two smooth low dimensional Anosov systems is absolutely continuous , then it is as smooth as the maps. We furthermore prove generalizations of thse facts for non-unifor...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2020
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2020.80