Topological speedups of ℤd-actions

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2022-02-06 DOI:10.1080/14689367.2022.2033166

Aimee S. A. Johnson, D. McClendon

引用次数: 1

Abstract

We study minimal -Cantor systems and the relationship between their speedups, their collections of invariant Borel measures, their associated unital dimension groups, and their orbit equivalence classes. In the particular case of minimal -odometers, we show that their bounded speedups must again be odometers but, contrary to the 1-dimensional case, they need not be conjugate, or even isomorphic, to the original. Furthermore, we give examples of speedups of -odometers which show the significant role played by a choice of ‘cone’ associated to the speedup.

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算子的拓扑加速

我们研究了最小-康托系统及其加速、不变Borel测度集合、相关单位维群和轨道等价类之间的关系。在最小-里程计的特殊情况下，我们证明了它们的有界加速度必须再次是里程计，但与一维情况相反，它们不必与原始情况共轭，甚至不同构。此外，我们给出了-里程表加速的例子，表明选择与加速相关的“锥”所起的重要作用。

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

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences