Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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TAME DIFFEOMORPHISMS WITH C1-STABLE PROPERTIES

  • Lee, Manseob (Department of Mathematics, Mokwon University)
  • Received : 2008.10.07
  • Accepted : 2008.11.20
  • Published : 2008.12.30
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Abstract

Let f be a diffeomorphisms of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper, we prove that if generically, f is tame diffeomorphims then the following conditions are equivalent: (i) f is ${\Omega}$-stable, (ii) f has the $C^1$-stable shadowing property (iii) f has the $C^1$-stable inverse shadowing property.

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