Limit weak shadowable transitive sets of $C^1$-generic diffeomorphisms

Manseob Lee; Gang Lu

doi:10.4134/CKMS.2012.27.3.613

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Commun. Korean Math. Soc. 2012; 27(3): 613-619

Printed September 1, 2012

https://doi.org/10.4134/CKMS.2012.27.3.613

Limit weak shadowable transitive sets of $C^1$-generic diffeomorphisms

Manseob Lee and Gang Lu

Mokwon University, ShenYang University of Technology

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Abstract

In this paper, we prove that locally maximal transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit weak shadowable.

Keywords: weak shadowing, limit weak shadowing, transitive set, hyperbolic, generic

MSC numbers: 37B20, 37C50, 37D30

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Limit weak shadowable transitive sets of $C^1$-generic diffeomorphisms

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