2023•Galore International Journal of Applied Sciences and HumanitiesOpen access

Topological Entropy and Topologically Mixing Property in b-Topological Spaces

Ahmed M. Rajab, OHOOD A. HADI, Ameer K. Abdulaal

Abstract

In this paper, we investigate the concepts of topological entropy (briefly top. ent.) and topologically mixing (briefly top. mix.) property in the context of b-topological spaces (briefly b- top. sps.). We introduce the notion of b-top. ent.as a measure of complexity for dynamical systems (briefly dy. sy.) defined on b-top. sps. We establish its properties and provide examples to illustrate its behavior. Furthermore, we define and study the top. mix. property in the setting of b-top. sps. and explore its connections with other dynamical properties. We present several results characterizing top. mix. and discuss its implications for the dynamics of b-topological systems. Keywords: b-Topological Spaces, Topological Entropy, Topologically Mixing Property, Dynamical Systems

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Key concepts: Topological entropy, Topological dynamics, Topological entropy in physics, Mixing (physics), Mathematics, Topological space, Topology (electrical circuits), Dynamical systems theory