Topological transitivity in quasi-continuous dynamical systems

A quasi-continuous dynamical system is a pair (X,f) consisting of a topological space X and a mapping f:X→X such that fn is quasi-continuous for all n∈N, where N is the set of non-negative integers. In this paper, we show that under appropriate assumptions, various definitions of the concept of topo...

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Bibliographic Details
Published in:Topology and its applications 2021-09, Vol.301, p.107496, Article 107496
Main Authors: Cao, Jiling, McCluskey, Aisling
Format: Article
Language:English
Subjects:
Dynamical system
Isolated point
Orbit
Point transitive
Quasi-continuous
Topological transitive
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Summary:A quasi-continuous dynamical system is a pair (X,f) consisting of a topological space X and a mapping f:X→X such that fn is quasi-continuous for all n∈N, where N is the set of non-negative integers. In this paper, we show that under appropriate assumptions, various definitions of the concept of topological transitivity are equivalent in a quasi-continuous dynamical system. Our main results establish the equivalence of topological and point transitivity in a quasi-continuous dynamical system. These extend some classical results on continuous dynamical systems in [3], [10] and [24], and some results on quasi-continuous dynamical systems in [7] and [8].
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2020.107496