Time Weighted Entropies And Sub-additive Topological Pressure Of The Noncompact System

We mainly study time weighted entropies, sub-additive topological pres-sure and a multi-fractal analysis of the entropy spectra of generalized Birkhoff averages in the noncompact system in this paper, main results are as follows:1. We introduce several reasonable definitions of time weighted entropies of the noncompact system. Furthermore, we investigate the relations between time weighted entropies of the original system and its one-point compactification. As a corollary, some properties of time weighted entropies of the noncompact system are given.2. We give the reasonable definition of sub-additive topological pressure of the noncompact system and discuss some corresponding properties. Then we study the relations between sub-additive topological pressure of the original system and its one-point compactification. Moreover, we present the variational principle and inverse variational principle of sub-additive topological pressure of the noncompact system.3. We describe a multi-fractal analysis of the entropy spectra of generalized Birkhoff averages in the noncompact system.