대한수학회지 (Journal of the Korean Mathematical Society)

  • 제59권2호
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  • Pages.337-352
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  • 2022
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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HISTORIC BEHAVIOR FOR FLOWS WITH THE GLUING ORBIT PROPERTY

  • 투고 : 2021.04.10
  • 심사 : 2021.12.06
  • 발행 : 2022.03.01
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초록

We consider the set of points with historic behavior (which is also called the irregular set) for continuous flows and suspension flows. In this paper under the hypothesis that (Xt)t is a continuous flow on a d-dimensional Riemaniann closed manifold M (d ≥ 2) with gluing orbit property, we prove that the set of points with historic behavior in a compact and invariant subset ∆ of M is either empty or is a Baire residual subset on ∆. We also prove that the set of points with historic behavior of a suspension flows over a homeomorphism satisfyng the gluing orbit property is either empty or Baire residual and carries full topological entropy.

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과제정보

The author is deeply grateful to Paulo Varandas, Thiago Bomfim and Diego Daltro for the incentive and suggestions that helped to improve the structure of the paper.

참고문헌

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