Topological transitivity in quasi-continuous dynamical systems

Abstract

A quasi-continuous dynamical system is a pair $(X,f)$ consisting of a topological space $X$ and a mapping $f:X\to X$ such that $f^n$ is quasi-continuous for all $n\in \mathbb{N}$, 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].

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References in corpus (1)

• Dynamics of Discontinuous Maps Via Closed Relations