Topological Entropy And Its Role In Weight Semigroups Fractal Analysis

This thesis investigates some problems of the topological entropy of a semi-group of maps in topological dynamical sys-tems、multifractal analysis and topological pressure of subadditive potentials. In the first part of the thesis, we will define three kinds of topological entropy of a semi-group of maps and give its relation and properties. In the second part, we will intruduce the Multifractal analysis of local entropies of a semi-group for recurrence time. In the third part,we will prove the main theorem of topological pressure for subadditive potentials. The paper is organized as followsIn chapter1:the development and some results of the topo-logical entropy of a semi-group of maps; the Multifractal analysis of local entropies and topological pressure for subadditive potentials are reviewed.In chapter2:we recall some classical definitions and theory.In chapter3:we will define three kinds of topological entropy of a semi-group of maps and give its relation and properties.In chapter4: We consider the multifractal analysis of local en-tropies of a semi-group for recurrence time. Futhermore we show the connections between the topological entropy and (q, Γ)-entropy of a semi-group of maps for level set Kα. For any α≥0, q∈R,we haveIn chapter5:we will give and prove the main theorem of topo-logical pressure for subadditive potentials.