relative information functional of relative dynamical systems

in this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. we extract the information function ofan ergodic dynamical system (x,t) from the relative information of t fromthe view point of observer χx, where x denotes the base space of the system.we also generalize the invariance of the information function of a dynamicalsystem , under topological isomorphism, to the relative information functional.