Topological and symbolic dynamics for hyperbolic systems with holes

Abstract

AbstractWe 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.