Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(1): 149-157

Printed January 31, 2015

https://doi.org/10.4134/BKMS.2015.52.1.149

Copyright © The Korean Mathematical Society.

Shadowable chain components and hyperbolicity

Manseob Lee, Seunghee Lee, and Junmi Park

Mokwon University, Chungnam National University, Chungnam National University

Abstract

We show that $C^1$-generically, the shadowable chain component of a $C^1$-vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.

Keywords: hyperbolic, shadowable, chain component

MSC numbers: Primary 37C50; Secondary 34D10

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