Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations Pub Date : 2024-02-10 DOI:10.1007/s10884-023-10344-5

引用次数: 0

Abstract

Let N be an n-dimensional compact riemannian manifold, with \(n\ge 2\) . In this paper, we prove that for any \(\alpha \in [0,n]\) , the set consisting of homeomorphisms on N with lower and upper metric mean dimensions equal to \(\alpha \) is dense in \(\text {Hom}(N)\) . More generally, given \(\alpha ,\beta \in [0,n]\) , with \(\alpha \le \beta \) , we show the set consisting of homeomorphisms on N with lower metric mean dimension equal to \(\alpha \) and upper metric mean dimension equal to \(\beta \) is dense in \(\text {Hom}(N)\) . Furthermore, we also give a proof that the set of homeomorphisms with upper metric mean dimension equal to n is residual in \(\text {Hom}(N)\) .

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同构公制平均维度水平集的密度

Abstract Let N be an n-dimensional compact riemannian manifold, with \(n\ge 2\) .在本文中，我们证明了对于任意一个（在 [0,n]\ 中的）N 上的同构，其上下度量平均维数等于（\alpha \）的集合在（\text {Hom}(N)\) 中是密集的。更一般地说，给定 \(alpha ,\beta \in [0,n]\), with \(alpha \le \beta \), 我们证明了由 N 上下层度量平均维度等于 \(alpha \)和上层度量平均维度等于 \(beta \)的同构组成的集合在 \(\text {Hom}(N)\) 中是密集的。此外，我们还证明了上度量平均维度等于 n 的同构集合在（text {Hom}(N)\) 中是残余的。

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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来源期刊

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.