Historic behavior for flows with the gluing orbit property. (English) Zbl 1495.37040
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 \((X_t)_t\) 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.
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| [19] | Heides Lima de Santana Instituto Federal da Bahia -IFBA, BR 116 Norte, Km-220, CEP: 48500-000, Euclides da Cunha-Bahia, Brazil Email address: heideslima@gmail.com |
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