We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e., dimK u a =DimK u a =f(a), wheref is the multifractal sp...We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e., dimK u a =DimK u a =f(a), wheref is the multifractal spectral function of the directed graph self similar measure, Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping. Key words Hausdorff dimension - Hausdorff measure - multifractal decomposition CLC number O 211. 6 Foundation item: Supported by the National Natural Science Foundation of China (10371092) and the Foundation of Wuhan UniversityBiography: Zheng Shui-cao (1973-), male, Ph. D candidate, research direction: stochastic processes and random fractals.展开更多
Let K be a statistically self-similar set defined by Graf.In this paper,we construct a random measure ρ which is supported by K and study the multifractal decomposition for K with p. Under such a decomposition,we obt...Let K be a statistically self-similar set defined by Graf.In this paper,we construct a random measure ρ which is supported by K and study the multifractal decomposition for K with p. Under such a decomposition,we obtain the expression of the spectrum function f(α).展开更多
The characteristics of cookie-cutter sets in R^d are investigated. A Bowen's formula for the Hausdorff dimension of a cookie-cutter set in terms of the pressure function is derived. The existence of self-similar m...The characteristics of cookie-cutter sets in R^d are investigated. A Bowen's formula for the Hausdorff dimension of a cookie-cutter set in terms of the pressure function is derived. The existence of self-similar measures, conformal measures and Gibbs measures on cookie-cutter sets is proved. The dimension spectrum of each of these measures is analyzed. In addition, the locally uniformly a-dimensional condition and the fractal Plancherel Theorem for these measures are shown. Finally, the existence of order-two density for the Hausdorff measure of a cookie-cutter set is proved.展开更多
文摘We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e., dimK u a =DimK u a =f(a), wheref is the multifractal spectral function of the directed graph self similar measure, Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping. Key words Hausdorff dimension - Hausdorff measure - multifractal decomposition CLC number O 211. 6 Foundation item: Supported by the National Natural Science Foundation of China (10371092) and the Foundation of Wuhan UniversityBiography: Zheng Shui-cao (1973-), male, Ph. D candidate, research direction: stochastic processes and random fractals.
基金Research supported by National Natural Science Foundation of China (No.19671066)
文摘Let K be a statistically self-similar set defined by Graf.In this paper,we construct a random measure ρ which is supported by K and study the multifractal decomposition for K with p. Under such a decomposition,we obtain the expression of the spectrum function f(α).
基金supported by the National Natural Science Foundation of China.
文摘The characteristics of cookie-cutter sets in R^d are investigated. A Bowen's formula for the Hausdorff dimension of a cookie-cutter set in terms of the pressure function is derived. The existence of self-similar measures, conformal measures and Gibbs measures on cookie-cutter sets is proved. The dimension spectrum of each of these measures is analyzed. In addition, the locally uniformly a-dimensional condition and the fractal Plancherel Theorem for these measures are shown. Finally, the existence of order-two density for the Hausdorff measure of a cookie-cutter set is proved.
