The Role Of Topological Semigroup Dynamical System Pressure

This thesis investigates some problems of the topological pres-sure for semigroup actions and multifractal analysis of local packing entropies for recurrence time. The organization of this thesis is as follows:In chapter1, the development and some results of the pressure and multifractal analysis are reviewed.In chapter2, we recall some classical definitions and theory.In chapter3, we introduce a topological semigroup G on a metric space (X, p), Using the spanning set and separate set which definied by K. Hofmann and L. Stojanov [9]. From the point of view of the spanning set, separate set and open covers, we define the topological pressure of semigroup actions.In chapter4, we consider the multifractal analysis of local packing entropies for recurrence time. Futhermore we show the connections between the packing topological entropy and (q, r)-Packing entropy for level set Ka. For any a>0, q∈R, we have hptopp(f, Kα)=qα＋hτp(f, q,Ka).