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http://dx.doi.org/10.14403/jcms.2015.28.1.103

DYNAMICAL SYSTEMS WITH SPECIFICATION

Lee, Keonhee (Department of Mathematics Chungnam National University)
Tajbakhsh, Khosro (Department of Mathematics Tarbiat Modares University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.28, no.1, 2015 , pp. 103-108 More about this Journal

Abstract

In this paper we prove that $C^1$ -generically, if a diffeomorphism f on a closed $C^{\infty}$ manifold M satisfies weak specification on a locally maximal set ${\Lambda}{\subset}M$ then ${\Lambda}$ is hyperbolic for f. As a corollary we obtain that $C^1$ -generically, every diffeomorphism with weak specification is Anosov.

Keywords

generic; hyperbolic; shadowing; specification; weak specification;

Citations & Related Records

Reference

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