Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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CHAIN TRANSITIVE SETS AND DOMINATED SPLITTING FOR GENERIC DIFFEOMORPHISMS

  • Lee, Manseob (Department of Mathematics, Mokwon University)
  • Received : 2016.11.04
  • Accepted : 2017.02.01
  • Published : 2017.05.15
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Abstract

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.

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References

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