Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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UNIVERSALLY MEASURE CONTINUUM-WISE EXPANSIVE HOMOCLINIC CLASSES

  • Daejung Kim (Chungnam Middle School) ;
  • Seunghee Lee (Healthcare Data Science Center Konyang University Medical Center) ;
  • Junmi Park (Department of Mathematics Chungnam National University)
  • Received : 2023.06.22
  • Accepted : 2023.08.07
  • Published : 2023.08.31
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Abstract

Investigating local dynamics requires precise control to effectively manage the subtle differences that distinguish it from global dynamics. This paper aims to study the localized perspective of the recently proposed continuum-wise expansive measures [13]. Let f : M → M be a diffeomorphism on a closed smooth manifold M and let p be a hyperbolic periodic point of f. We prove that if the homoclinic class Hf (p) of f associated to p is C1-robustly measure continuum-wise expansive then it is hyperbolic.

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Acknowledgement

Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIT) (No. 2020R1F1A1A01073872 and No. 2021R1F1A1052631). Supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIT) (No. 2020R1I1A1A01069812).

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