2020/07/25 by Jiling Cao, Cao, Jiling, Aisling McCluskey +1
Mathematics · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.2007.13032
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 ∈ \mathbb N, where \mathbb 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 [25], and some results on quasi-continuous dynamical systems in [7] and [8].