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Topological and symbolic dynamics for hyperbolic systems with holes

Bundfuss, Stefan; Krüger, Tyll; Troubetzkoy, Serge

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 non-wandering set Ωnw. Our results are on the cardinality of the set of topologically transitive components of Ωnw and their structure. We also prove that Ω* is generically a subshift of finite type in several senses.
Published in: Ergodic theory and dynamical systems, 10.1017/s0143385710000556, Cambridge University Press
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  • This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.