Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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STABILITY OF WEAK MEASURE EXPANSIVE DIFFEOMORPHISMS

  • Ahn, Jiweon (Department of Mathematics Chungnam National University) ;
  • Kim, Soyean (Department of Mathematics Daejeon University)
  • Received : 2017.09.19
  • Accepted : 2018.03.07
  • Published : 2018.09.01
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Abstract

A notion of measure expansivity for homeomorphisms was introduced by Morales recently as a generalization of expansivity, and he obtained many interesting dynamic results of measure expansive homeomorphisms in [8]. In this paper, we introduce a concept of weak measure expansivity for homeomorphisms which is really weaker than that of measure expansivity, and show that a diffeomorphism f on a compact smooth manifold is $C^1$-stably weak measure expansive if and only if it is ${\Omega}$-stable. Moreover we show that $C^1$-generically, if f is weak measure expansive, then f satisfies both Axiom A and the no cycle condition.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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