relative information functional of relative dynamical systems

In this paper by use of mathematical modeling of an observer the notion of relative information functional for relative dynamical systems on compact metric spaces is presented. we extract the information function of an ergodic dynamical system (x; t) from the relative information of t from the view point of observer x, where x denotes the base space of the system. we also generalize the invariance of the information function of a dynamical system , under topological isomorphism, to the relative information functional.