Topological entropy of nonautonomous dynamical systems on uniform spaces

In this paper, we focus on some properties, calculations and estimations of topological entropy for a nonautonomous dynamical system (X,f0,∞) generated by sequence continuous self-maps f0,∞={fn}n=0∞ compact uniform space X. We prove that its k-th product have the same entropy. confirm equals to n-th compositions system, also f0,∞ restricted non-wandering set if is equi-continuous. less than or equal limit (X,f) when converges uniformly f. show two topologically equi-semiconjugate systems equi-semiconjugacy finite-to-one. Finally, obtain upper lower bounds an invariant subsystem coupled-expanding associated with transition matrix.