HISTORIC BEHAVIOR FOR FLOWS WITH THE GLUING ORBIT PROPERTY

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 tha...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 59; no. 2; pp. 337 - 352
Main Author de Santana, Heides Lima
Format Journal Article
LanguageKorean
Published 2022
Subjects
Historic behavior
flows
suspension flows
gluing orbit property
irregular set
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Summary: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.
Bibliography:KISTI1.1003/JNL.JAKO202209748274299
ISSN:0304-9914