Return To The Entropy Of The Fractal Spectrum Valuation And Functions Column On Local Entropy Of High Dimensional Multifractal Analysis

In this paper,we address the problem of the estimate on the multifractal spectrum of local entropies for recurrence time and also study the higher multifractal analysis of local entropy for function sequences.In chapter one, we introduced some basic concepts of multifractal analysis and the background of the thesis. In chapter two, we mainly study the problem of the estimate on the multifractal spectrum of local entropies for recurrence time. The domain and the upper estimate of the multifractal spectrum are given.In chapte three, we study the higher multifractal analysis of local entropy for function sequences. We define the ( q₁ ,q₂,f,g)-entropy for these functions and give the relation between the topological entropy and ( q₁ ,q₂,f,g)-entropy for the level set.