Topological and symbolic dynamics for hyperbolic systems with holes
نویسندگان
چکیده
منابع مشابه
Topological and Symbolic Dynamics for Hyperbolic Systems with Holes
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 consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of Ω. Our main result are that each topologically transitive component of Ω is coded and that typically Ω is of finite type.
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◦ 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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We consider an Axiom A diffeomorphism and the invariant set of orbits which never falls into a fixed hole. We study various aspects of the complexity of the symbolic representation of Ω. Our main result are that each topologically transitive component of Ω is coded and that typically Ω is of finite type.
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We study the action of a relatively hyperbolic group on its boundary, by methods of symbolic dynamics. Under a condition on the parabolic subgroups, we show that this dynamical system is finitely presented. We give examples where this condition is satisfied, including geometrically finite kleinian groups. Associated to any word-hyperbolic group Γ, there is a dynamical system arising from the ac...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2010
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385710000556