Relative Entropy Functional of Relative Dynamical Systems

Abstract

In this paper, the notion of the relative entropy functional for relative dynamical systems on compact metric spaces is presented using the mathematical modeling of an observer. The invariance of the entropy of a system under topological conjugacy to the relative entropy functional is generalized. A new version of Jacobs Theorem concerning the entropy of a dynamical system is given. At the end, the Kolmogorov entropy from the relative entropy functional for dynamical systems from the view point of observer χX , where X denotes the base space of the system, is extracted.

Keywords

• : Entropy,relative dynamical system,invariant,relative generator,relative measure,relative entropy

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