Relative topological conditional entropy and a Ledrappier's type variational principle for it

In this paper we provide a sufficient condition for the existence of invariant measures with maximal relative measure-theoretic entropy, by introducing new any factor map between topological dynamical systems, concept conditional entropy. It is proved Ledrappier's type variational principle concerning Consequently, if has zero entropy (such called asymptotically $ h $-expansive), then there exist (i.e., whose equals exactly map). We explore further properties example, addition formula product map, estimation it composition two maps, and so on. also interpret respectively, using subsets Bowen's dimensional