Topological and Symbolic Dynamics for Axiom A Diffeomorphisms with Holes

Details Topological and Symbolic Dynamics for Axiom A Diffeomorphisms with Holes Topological and Symbolic Dynamics for Axiom A Diffeomorphisms with Holes

2001-01-16

arxiv.org/abs/math/0101128v2

Mathematics

Dynamical Systems

17 pages, no figures

Scientific paper

We consider an Axiom A diffeomorphism and the invariant set $\Omega$ of
orbits which never falls into a fixed hole. We study various aspects of the
complexity of the symbolic representation of $\Omega$. Our main result are that
each topologically transitive component of $\Omega$ is coded and that typically
$\Omega$ is of finite type.

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