On two notions of expansiveness for continuous semiflows

Sebastián Herrero, Nelda Jaque

Research output: Contribution to journalArticlepeer-review

Abstract

We study two notions of expansiveness for continuous semiflows: expansiveness in the sense of Alves, Carvalho and Siqueira (2017), and an adaptation of positive expansiveness in the sense of Artigue (2014). We prove that if X is a metric space and ϕ is an expansive semiflow on X according to the first definition, then the semiflow ϕ is trivial and the space X is uniformly discrete. In particular, if X is compact then it is finite. With respect to the second definition, we prove that if X is a compact metric space and ϕ is a positive expansive semiflow on it, then X is a union of at most finitely many closed orbits, unbranched tails and isolated singularities.

Original languageEnglish
Article number126405
JournalJournal of Mathematical Analysis and Applications
Volume515
Issue number1
DOIs
StatePublished - 1 Nov 2022
Externally publishedYes

Keywords

  • Continuous semiflows
  • Expansiveness

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