Topological Entropy and Topologically Mixing Property in b-Topological Spaces
Ahmed M. Rajab, Ohood Ayyed Hadi, Ameer K. Abdulaal · Galore International Journal of Applied Sciences and Humanities · 2023
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