Uosef mohammadi

In this paper, the concept of weighted entropy function for dynamical systems on compact metric spaces is introduced using the generator notion. It is proved that this concept is an extension of the Kolmogorov-Sinai entropy. The independence of weighted entropy function of generators is proved. The persistence of weighted entropy function under a topological conjugate relation is deduced. A version of Jacobs Theorem concerning the entropy of a dynamical system is given. Moreover it is shown that weighted entropy function generates the Kolmogorov-Sinai entropy as a special case.