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Topological and symbolic dynamics for hyperbolic systems with holes

Published online by Cambridge University Press:  17 November 2010

STEFAN BUNDFUSS
Affiliation:
Department of Mathematics, Technische Universität Darmstadt, Germany (email: bundfuss@mathematik.tu-darmstadt.de)
TYLL KRÜGER
Affiliation:
FB Mathematik, Technische Universität Berlin and Fakultät für Physik, Universität Bielefeld, Germany (email: tkrueger@math.tu-berlin.de)
SERGE TROUBETZKOY
Affiliation:
Centre de Physique Théorique, Fédération de Recherche des Unités Mathématiques de Marseille, Institut de Mathématiques de Luminy, and Université de la Méditerranée, Marseille, France (email: troubetz@iml.univ-mrs.fr)

Abstract

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.

Type
Research Article
Copyright
Copyright © Cambridge University Press 2010

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