Equicontinuity, transitivity and sensitivity: the Auslander-Yorke dichotomy revisited

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
88 Downloads (Pure)

Abstract

We study sensitivity, topological equicontinuity and even continuity in dynamical systems. In doing so we provide a classification of topologically transitive dynamical systems in terms of equicontinuity pairs, give a generalisation of the Auslander-Yorke dichotomy for minimal systems and show there exists a transitive system with an even continuity pair but no equicontinuity point. We define what it means for a system to be eventually sensitive; we give a dichotomy for transitive dynamical systems in relation to eventual sensitivity. Along the way we define a property called splitting and discuss its relation to some existing notions of chaos. The approach we take is topological rather than metric.
Original languageEnglish
Pages (from-to)2441-2474
Number of pages34
JournalDiscrete and Continuous Dynamical Systems
Volume40
Issue number4
DOIs
Publication statusPublished - 30 Apr 2020

Keywords

  • equicontinuity
  • even continuity
  • topological transitivity
  • sensitivity
  • chaos
  • Auslander-Yorke dichotomy
  • minimality

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Equicontinuity, transitivity and sensitivity: the Auslander-Yorke dichotomy revisited'. Together they form a unique fingerprint.

Cite this