CHAIN TRANSITIVE SETS AND DOMINATED SPLITTING FOR GENERIC DIFFEOMORPHISMS

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Published: May 15, 2017
DOI: https://doi.org/10.14403/jcms.2017.30.2.177
Keywords:
chain transitive, generic, locally maximal, dominated splitting, zero entropy
Mathematics Subject Classification (2020):
Primary 37D30

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Manseob Lee
Department of Mathematics, Mokwon University,

Abstract





Let f : M ! M be a diffeomorphism of a compact smooth manifold M . In this paper, we show that C 1 generically, if a chain transitive set * is locally maximal then it admits a dominated splitting. Moreover, C 1 generically if a chain transitive set * of f is locally maximal then it has zero entropy.





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Article Details

Issue
Vol. 30 No. 2 (2017)
Section
Articles