Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2016; 31(2): 389-394

Printed April 30, 2016

https://doi.org/10.4134/CKMS.2016.31.2.389

Copyright © The Korean Mathematical Society.

The local star condition for generic transitive diffeomorphisms

Manseob Lee

Mokwon University

Abstract

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Let $f:M\to M$ be a diffeomorphism on a closed $C^{\infty}$ $d(\geq2)$ dimensional manifold $M$. For $C^1$-generic $f$, if a diffeomorphism $f$ satisfies the local star condition on a transitive set, then it is hyperbolic.

Keywords: transitive set, star diffeomorphisms, local star diffeomorphisms, hyperbolic

MSC numbers: 37D20, 37C75

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