Multifractal Analysis Of Local Entropy For A Sequence Of Functions And Topological Sequence Pressure

In this paper, we study the multifractal analysis of local entropy and topological sequence pressure.In preface, we introduced some basic concepts of multifractal analysis and topological entropy.In chapter one, we mainly study multifractal analysis of local entropy. Historically, multifractal analysis was mainly concerned with the study of local dimension of a Borel measure μ. In this section we consider a sequence of functions. These functions are set-valued functions and have the similar properties with Borel measure μ. We define the (q, f)-entropy for these functions and give the relation between the topological entropy and (q, f)-entropy for the level set K_α.In chapter two, we introduce the definition and study some properties of topological sequence pressure based on the definition of topological sequence, entropy and measure sequence entropy.