Mandelbrot乘法级联的傅立叶维数

IF 2.6 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-07-02 DOI:10.1007/s00220-025-05354-x

Changhao Chen, Bing Li, Ville Suomala

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引用次数: 0

摘要

我们研究了d维单位立方上Mandelbrot乘法级联测度$\mu $的傅里叶维，$\dim _F\mu $。我们表明，如果$\mu $是由次指数随机变量产生的级联度量，那么$$\begin{aligned} \dim _F\mu =\min \{2,\dim _2\mu \}, \end{aligned}$$，其中$\dim _2\mu $是$\mu $的相关维数，并且它有一个显式公式。对于圆$S\subset \mathbb {R}^2$上的级联，我们得到 $$\begin{aligned} \dim _F\mu \ge \frac{\dim _2\mu }{2+\dim _2\mu }. \end{aligned}$$

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Fourier Dimension of Mandelbrot Multiplicative Cascades

We investigate the Fourier dimension, $\dim _F\mu $, of Mandelbrot multiplicative cascade measures $\mu $ on the d-dimensional unit cube. We show that if $\mu $ is the cascade measure generated by a sub-exponential random variable, then

$$\begin{aligned} \dim _F\mu =\min \{2,\dim _2\mu \}, \end{aligned}$$

where $\dim _2\mu $ is the correlation dimension of $\mu $ and it has an explicit formula. For cascades on the circle $S\subset \mathbb {R}^2$, we obtain

$$\begin{aligned} \dim _F\mu \ge \frac{\dim _2\mu }{2+\dim _2\mu }. \end{aligned}$$

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.