Research Paper
Year: 2023 | Month: July-September | Volume: 7 | Issue: 3 | Pages: 38-49
DOI: https://doi.org/10.52403/gijash.20230305
Topological Entropy and Topologically Mixing Property in b-Topological Spaces
AHMED M. RAJAB1, OHOOD A. HADI2, AMEER K. ABDULAAL3
1,2Department of Mathematics,
Faculty of Computer Sciences and Mathematics, University of KUFA, Kufa, Najaf, IRAQ.
3Ministry of Education/Najaf Education Directorate,
Corresponding Author: Ahmed M. Rajab
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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