IJPAM: Volume 115, No. 1 (2017)

Title

SHADOWABLE WEAKLY TRANSITIVE SETS
ARE HYPERBOLIC

Authors

Manseob Lee
Department of Mathematics
Mokwon University
Daejeon, 302-729, KOREA

Abstract

Let $M^d(d\geq2)$ be a closed smooth manifold, and let $f$ be a diffeomorphism on $M.$ Let $\Lambda$ be a weakly transitive set for $f$. First, we show that $f$ has the $C^1$-stably shadowing property on $\Lambda$ if and only if $\Lambda$ is a hyperbolic basic set. Finally, we prove that for $C^1$-generic $f,$ a locally maximal weakly transitive set is shadowable if and only if that weakly transitive set is a hyperbolic basic set.

History

Received: March 3, 2017
Revised: June 28, 2017
Published: June 29, 2017

AMS Classification, Key Words

AMS Subject Classification: 37C20, 37C25, 37C50, 34D10
Key Words and Phrases: shadowing, hyperbolic, weakly transitive, transitive set, basic set

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How to Cite?

DOI: 10.12732/ijpam.v115i1.13 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 1
Pages: 169 - 186


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