Conditional Variational Principle Of Packing Pressure And Packing Entropy Of Factor Mapping

We study the relation between packing topological pressure and upper capacity topological pressure with a factor map in topologi-cal dynamical systems.we obtain a variational principle of packing entropy in multifractal analysis. In the first part of the thesis, we define packing topological pressure, upper capacity topological pres-sure and study the relation between packing topological pressure and upper capacity topological pressure of subadditive potentials. In the second part, we review some basic notions in multifractal analysis and obtain the variational principle of packing topological entropy.The paper is organized as follows:In Chapter 1, the backgrounds of topological entropy, topological pressure and multifractal analysis are introduced.In Chapter 2, some basic notions and results in topological dy-namical systems and ergodic theory which will be used in thesis, are reviewed.In Chapter 3, we define several types of topological pressure of subadditive potentials and study the relation between packing topo-logical pressure and upper capacity topological pressure of subaddi-tive potentials.In Chapter 4, we review some classical definitions in multifractal analysis and show the variational principle of packing topological entropy.