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 language | English |
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Pages (from-to) | 2441-2474 |
Number of pages | 34 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 40 |
Issue number | 4 |
DOIs | |
Publication status | Published - 30 Apr 2020 |
Keywords
- Auslander-Yorke dichotomy
- chaos
- equicontinuity
- even continuity
- minimality
- sensitivity
- topological transitivity
ASJC Scopus subject areas
- General Mathematics