Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2022; 59(2): 337-352

Online first article March 1, 2022      Printed March 1, 2022

https://doi.org/10.4134/JKMS.j210245

Copyright © The Korean Mathematical Society.

Historic behavior for flows with the gluing orbit property

Heides Lima de Santana

Instituto Federal da Bahia - IFBA, BR 116 Norte, Km-220,

Abstract

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 $(X_t)_t$ is a continuous flow on a $d$-dimensional Riemaniann closed manifold $M$ $(d \geq 2)$ with gluing orbit property, we prove that the set of points with historic behavior in a compact and invariant subset $\Delta$ of $M$ is either empty or is a Baire residual subset on $\Delta$. 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.

Keywords: Historic behavior, irregular set, flows, suspension flows, gluing orbit property

MSC numbers: 37E45, 37E35, 37C10, 37C50

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