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Topologically Stable Chain Recurrence Classes for Diffeomorphisms

Author

Listed:
  • Manseob Lee

    (Department of Mathematics, Mokwon University, Daejeon 302-729, Korea)

Abstract

Let f : M → M be a diffeomorphism of a finite dimension, smooth compact Riemannian manifold M . In this paper, we demonstrate that if a diffeomorphism f lies within the C 1 interior of the set of all chain recurrence class-topologically stable diffeomorphisms, then the chain recurrence class is hyperbolic.

Suggested Citation

  • Manseob Lee, 2020. "Topologically Stable Chain Recurrence Classes for Diffeomorphisms," Mathematics, MDPI, vol. 8(11), pages 1-6, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1912-:d:438544
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