arXiv 0806.12762008-06-07math.DS

Multifractal Formalism and Inequality involving Packing Dimension

Leila Ben Youssef

备注：: 16pages

英文摘要：

This article fits in many studies of multifractal analysis of measure. We took as a starting point the work of F. Ben Nasr in " Calculs de dimension de packing " to give a new inequality involving $Dim(\bar{X}^α)$ which would be, in certain cases, finer than the inequality established by L. Olsen in " A multifractal formalism " . Besides we elaborated an application of our result which gives a better inequality involving $Dim(\bar{X}^α)$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Upper bounding for packing dimension in vectorial multifractal formalism

We establish an other upper bounding for packing dimension in the framework of the vectorial multifractal formalism that is in some cases finer than that established by J. Peyriere.

2011-01-12math.DS

多重分形拓扑熵的可测性及其在多重分形理论中的作用

Measurability of Multifractal Topological Entropy and Its Role in Multifractal Theory

本文研究$(q, \vartheta)$-Bowen和$(q, \vartheta)$-packing拓扑熵的性质与可测性，揭示其与水平集拓扑熵的关系，并证明packing熵定义域覆盖局部熵多重分形谱，为多重分形分析提供新工具。

2025-02-28math.DS

Multifractal analysis of random weak Gibbs measures

We describe the multifractal nature of random weak Gibbs measures on some class of attractors associated with $C^1$ random dynamics semi-conjugate to a random subshift of finite type. This includes the validity of the multifractal formalism, the calculation of Hausdorff and packing dimensions of the so-called level sets of divergent points, and a $0$-$\infty$ law for the Hausdorff and packing measures of the level sets of the local dimension.

2016-07-31math.DS

A multifractal formalism for Hewitt-Stromberg measures

In the present work, we give a new {\it multifractal formalism} for which the classical multifractal formalism does not hold. We precisely introduce and study a multifractal formalism based on the Hewitt-Stromberg measures and that this formalism is completely parallel to Olsen's multifractal formalism which based on the Hausdorff and packing measures.

2019-10-08math.DS

Multifractal spectra of Moran measures without local dimension

A measure without local dimension is a measure such that local dimension does not exist for any point in its support. In this paper, we construct such a class of Moran measures and study their lower and upper local dimensions. We show that the related "free energy" function ($L^q$-spectrum) does not exist. Nevertheless, we can obtain the full Hausdroff and packing dimension spectra for level sets defined by lower and upper local dimensions. They can be viewed as a generalized multifractal formalism.

2018-11-13math.DS

多重分形水平集与带势的度量平均维数

Multifractal level sets and metric mean dimension with potential

针对具有规范性质的动力系统，本文为多重分形水平集建立了带势的上、下Bowen/packing度量平均维数的条件变分原理。

2024-07-21math.DS

更多相关论文收起更多论文

The packing spectrum for Birkhoff averages on a self-affine repeller

We consider the multifractal analysis for Birkhoff averages of continuous potentials on a self-affine Sierpiński sponge. In particular, we give a variational principal for the packing dimension of the level sets. Furthermore, we prove that the packing spectrum is concave and continuous. We give a sufficient condition for the packing spectrum to be real analytic, but show that for general Hölder continuous potentials, this need not be the case. We also give a precise criterion for when the packing spectrum attains the full packing dimension of the repeller. Again, we present an example showing …

2011-03-24math.DS

A mixed multifractal analysis for quasi Ahlfors vector-valued measures

The multifractal formalism for measures in its original formulation is checked for special classes of measures such as doubling, self-similar, and Gibbs-like ones. Out of these classes, suitable conditions should be taken into account to prove the validity of the multifractal formalism. In the present work, a large class of measures satisfying a weak condition known as quasi Ahlfors is considered in the framework of mixed multifractal analysis. A joint multifractal analysis of finitely many quasi Ahlfors probability measures is developed. Mixed variants of multifractal generalizations of Hausd…

2021-03-07math.DSmath.MGmath.PR

Packing topological entropy for amenable group actions

Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as a counterpart of Bowen topological entropy. In the present paper, we will give a systematically study to the packing topological entropy for a continuous $G$-action dynamical system $(X,G)$, where $X$ is a compact metric space and $G$ is a countable discrete amenable group. We first prove a variational principle for amenable packing topological entropy: for any Borel subset $Z$ of $X$, the packing topological entropy of $Z$ equals the supremum of upper local entropy over all Borel probability me…

2021-09-28math.DS

On the $L^q$-spectrum of planar self-affine measures

We study the dimension theory of a class of planar self-affine multifractal measures. These measures are the Bernoulli measures supported on box-like self-affine sets, introduced by the author, which are the attractors of iterated function systems consisting of contracting affine maps which take the unit square to rectangles with sides parallel to the axes. This class contains the self-affine measures recently considered by Feng and Wang as well as many other measures. In particular, we allow the defining maps to have non-trivial rotational and reflectional components. Assuming the rectangular…

2013-10-15math.DS