DYNAMICAL SYSTEMS WITH SPECIFICATION

Abstract

In this paper we prove that C 1-generically, if a diffeomorphism f on a closed C∞ manifold M satisfies weak specification on a locally maximal set Λ ⊂ M then Λ is hyperbolic for f . As a corollary we obtain that C 1-generically, every diffeomorphism with weak specification is Anosov.

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