Shadowable chain components and hyperbolicity
Bull. Korean Math. Soc. 2015 Vol. 52, No. 1, 149-157
https://doi.org/10.4134/BKMS.2015.52.1.149
Printed January 31, 2015
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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