On entropy of pairwise continuous map in bitopological dynamical systems

Abstract

Topological entropy is an important and widely used measure of complexity in topological dynamical system where only one topology is involved in the entire mathematical process. Bitopological dynamical system is a new area of dynamical system to investigate dynamical properties in terms of a bitopological space which involves two topologies. In this paper we introduce entropy in bitopological dynamical system as a measure of complexity and produce some results related to entropy. Also, we introduce weighted bitopological Shannon entropy as an extension of Shannon entropy in information theory. Recently, Acharjee et al. (S. Acharjee, K. Goswami, HK. Sarmah, on forward iterated Hausdorffness and development of embryo from zygote in bitopological dynamical systems (communicated)) proved that the postgastrulation part of human embryo development is a bitopological dynamical system. As an application of our theory, we find bitopological entropy of the mitosis map in the bitopological space of postgastrulation part of human embryo development. Also, we find the weighted bitopological Shannon entropy in this space.