# HYPERBOLICITY OF CHAIN TRANSITIVE SETS WITH LIMIT SHADOWING

• Fakhari, Abbas (Department of Mathematics Shahid Beheshti University) ;
• Lee, Seunghee (Department of Mathematics Chungnam National University) ;
• Tajbakhsh, Khosro (Department of Mathematics Faculty of Mathematical Sciences Tarbiat Modares University)
• Received : 2011.06.02
• Published : 2014.09.30

#### Abstract

In this paper we show that any chain transitive set of a diffeomorphism on a compact $C^{\infty}$-manifold which is $C^1$-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.

#### Acknowledgement

Supported by : KRF

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