DOI QR코드

DOI QR Code

CHAIN TRANSITIVE SETS AND DOMINATED SPLITTING FOR GENERIC DIFFEOMORPHISMS

  • Lee, Manseob (Department of Mathematics, Mokwon University)
  • 투고 : 2016.11.04
  • 심사 : 2017.02.01
  • 발행 : 2017.05.15

초록

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

키워드

참고문헌

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피인용 문헌

  1. EVENTUAL SHADOWING FOR CHAIN TRANSITIVE SETS OF C1 GENERIC DYNAMICAL SYSTEMS vol.58, pp.5, 2021, https://doi.org/10.4134/jkms.j190083