STABLY PERIODIC SHADOWING AND DOMINATED SPLITTING

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Published: Nov 15, 2011
DOI: https://doi.org/10.14403/jcms.2011.24.4.735
Keywords:
periodic shadowing property, C 1-stably periodic shadowing property, pre-sink, pre-source, dominated splitting
Mathematics Subject Classification (2020):
Primary 37C20, 37C05, 37C29, 37D05

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Keonhee Lee
Department of Mathematics, Chungnam University
Manseob Lee
Department of Mathematics, Mokwon University
Jiweon Ahn
Department of Mathematics, Chungnam University

Abstract





Let f be a diffeomorphism of a closed n-dimensional In this paper, we introduce the notion of C 1smooth manifold. stably periodic shadowing property for a closed f -invariant set, and prove that for a transitive set Λ, if f has the C 1-stably periodic shadowing property on Λ, then Λ admits a dominated splitting.





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Article Details

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