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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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