The relations between the multifractal packing dimension of Borel probability measures and the asymptotic behavior of the function Ф＊（x）=limsup logv（B（x,r））-qlogu（B（x,r））/logr are discussed and some appli...The relations between the multifractal packing dimension of Borel probability measures and the asymptotic behavior of the function Ф＊（x）=limsup logv（B（x,r））-qlogu（B（x,r））/logr are discussed and some applications are given.展开更多
The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Ha...The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.展开更多
In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of...In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of orthogonal projections´of a couple of measures(µ,ν)in R^(n).As an application,we study the mutual multifractal analysis of the projections of measures.展开更多
基金Supported by the Education Committee of Fujian Province(JA08155)
文摘The relations between the multifractal packing dimension of Borel probability measures and the asymptotic behavior of the function Ф＊（x）=limsup logv（B（x,r））-qlogu（B（x,r））/logr are discussed and some applications are given.
文摘The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.
文摘In this paper,we compare the mutual multifractal Renyi dimensions to the´mutual multifractal Hausdorff and pre-packing dimensions.We also provide a relationship between the mutual multifractal Renyi dimensions of orthogonal projections´of a couple of measures(µ,ν)in R^(n).As an application,we study the mutual multifractal analysis of the projections of measures.
