展开马尔可夫映射的Lipschitz函数下循环和收缩目标集的Hausdorff维数

Pub Date : 2023-02-24 DOI:10.1080/14689367.2023.2184328

Na Yuan, Bing Li

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引用次数: 2

摘要

设T是一个扩展的马尔可夫映射，在上面定义了一个排斥者E。本文研究集合的Hausdorff维数，其中是具有一致Lipschitz常数的Lipschitz函数序列，f是在上定义的正连续函数，是和，ψ是在上定义的正函数。所得结果可应用于切饼动力系统和连分数动力系统等。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps

Let T be an expanding Markov map with a repeller E defined on . This paper concerns the Hausdorff dimension of the sets and where is a sequence of Lipschitz functions with a uniform Lipschitz constant, , f is a positive continuous function on , is the sum and ψ is a positive function defined on . The results can be applied to cookie-cutter dynamical systems and continued fraction dynamical systems, etc.

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