非自治康托尔集上的调和度量维数

arXiv - MATH - Probability Pub Date : 2024-09-12 DOI:arxiv-2409.08019

Athanasios Batakis, Guillaume Havard

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引用次数: 0

摘要

我们考虑非自治共形迭代函数系统（NACIFS）及其极限集。我们主要关注调和度量及其维度：Hausdorff 和 Packing。我们证明这两个维度在扰动下是连续的，而且它们验证了鲍温和曼宁类型公式。为此，我们证明了定义在符号空间上的度量的一般结果，以及更广义的正函数的一般结果，并在非自治环境中开发了热力学形式主义的工具。

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Dimensions of harmonic measures on non-autonomous Cantor sets

We consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and their limit set. Our main concern is harmonic measure and its dimensions : Hausdorff and Packing. We prove that this two dimensions are continuous under perturbations and that they verify Bowen's and Manning's type formulas. In order to do so we prove general results about measures, and more generally about positive functionals, defined on a symbolic space, developing tools from thermodynamical formalism in a non-autonomous setting.

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arXiv - MATH - Probability

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