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On the Entropy of Continuous Flows with Uniformly Expansive Points and the Globalness of Shadowable Points with Gaps

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Abstract

In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a sufficient condition to obtain positive topological entropy. Moreover, we can deal with flows with singularities, showing that the existence of a non-wandering, non-critical, strongly-shadowable, and uniformly-expansive point implies the existence of a symbolic subshift. Finally, we discuss pointwise versions of some shadowing-type properties.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, Rio de Janeiro, 21945-970, Brazil

    E. Rego & A. Arbieto

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  1. E. Rego
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  2. A. Arbieto
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Correspondence to E. Rego.

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E. Rego was partially supported by CAPES, CNPq and FAPERJ from Brazil. A. Arbieto was partially supported by CNPq, FAPERJ and PRONEX/DS from Brazil.

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Rego, E., Arbieto, A. On the Entropy of Continuous Flows with Uniformly Expansive Points and the Globalness of Shadowable Points with Gaps. Bull Braz Math Soc, New Series 53, 853–872 (2022). https://doi.org/10.1007/s00574-022-00285-w

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  • DOI: https://doi.org/10.1007/s00574-022-00285-w

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