DIFFEOMORPHISMS WITH ROBUSTLY AVERAGE SHADOWING

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Published: Nov 15, 2011
DOI: https://doi.org/10.14403/jcms.2011.24.4.631
Keywords:
average shadowing, hyperbolic, chain component, homoclinic class, generic, stably hyperbolic
Mathematics Subject Classification (2020):
Primary 37C50, 37D20, Secondary 37C25

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Keonhee Lee
Department of Mathematics, Chungnam University
Manseob Lee
Department of Mathematics, Mokwon University
Gang Lu
Department of Mathematics, Chungnam National University

Abstract





In this paper, we prove that for C 1 generically, if every hyperbolic periodic point in a chain component is uniformly far away from being nonhyperbolic, and it is C 1-robustly average shadowable, then the chain component is hyperbolic.





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Article Details

Issue
Vol. 24 No. 4 (2011)
Section
Articles