Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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POSITIVELY WEAK MEASURE EXPANSIVE DIFFERENTIABLE MAPS

  • Ahn, Jiweon (Department of Mathematics Chungnam National University) ;
  • Lee, Manseob (Department of Mathematics Mokwon University)
  • Received : 2018.12.06
  • Accepted : 2020.03.05
  • Published : 2020.05.31
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Abstract

In this paper, we introduce the new general concept of usual expansiveness which is called "positively weak measure expansiveness" and study the basic properties of positively weak measure expansive C1-differentiable maps on a compact smooth manifold M. And we prove that the following theorems. (1) Let 𝓟𝓦𝓔 be the set of all positively weak measure expansive differentiable maps of M. Denote by int(𝓟𝓦𝓔) is a C1-interior of 𝓟𝓦𝓔. f ∈ int(𝓟𝓦𝓔) if and only if f is expanding. (2) For C1-generic f ∈ C1 (M), f is positively weak measure-expansive if and only if f is expanding.

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References

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