Entropy of a Pairwise Continuous Map in NWPC Bitopological Dynamical Systems

Abstract

Topological entropy is a measure of complexity in topological dynamical systems. Recently, Acharjee et al. [S. Acharjee, K. Goswami and H.K. Sarmah, Transitive maps in bitopological dynamical systems, Filomat. 35(6), 2011–21(2021)] introduced bitopological dynamical systems to study dynamical systems with respect to two topologies. Also, Acharjee et al. [S. Acharjee, K. Goswami and H.K. Sarmah, On entropy of pairwise continuous map in bitopological dynamical systems, Commun. Math. Biol. Neurosci. 2020(2020), Article ID 81.] introduced the notion of entropy in bitopological dynamical systems where the underlying bitopological space was considered as weakly pairwise compact. In this chapter, we introduce entropy in non-weakly pairwise compact bitopological dynamical systems (in short NWPC bitopological dynamical systems) as a measure of complexity and produce several new results related to entropy. Also, we discuss about the possible connection between the neural activity of the human brain and the entropy of a pairwise continuous map in NWPC bitopological dynamical systems.