Related Studies Of Topological Pressure And Topological Entropy For Proper System

This paper focuses on the non-additive topological pressure and conditional entropy of proper map on the locally compact separable metric space. We get the following conclusions which about the non-additive topological pressure and conditional entropy of non-compact map, the main contents are divided into three parts as follows:1. Giving the reasonable definition of non-additive topological pressure of proper system by using proper map and admissible cover, and related properties are studied. In particular, by the relationship between the original system and compactification system, the corresponding variational principle is given.2. The variational principle and the properties of equilibrium measure with respect to almost additive topological pressure of proper system are given. At the same time, this paper discusses regularity of almost additive topological pressure of proper system, particularly, we obtain the corresponding conditional variational principle inequality.3. Reasonable definition of conditional entropy of proper system is given, and giving some relevant properties.