Minimal subdynamics and minimal flows without characteristic measures

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2024-05-10 DOI:10.1017/fms.2024.41

Joshua Frisch, Brandon Seward, Andy Zucker

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引用次数: 0

Abstract

Given a countable group G and a G-flow X, a probability measure

$\mu $

on X is called characteristic if it is

$\mathrm {Aut}(X, G)$

-invariant. Frisch and Tamuz asked about the existence of a minimal G-flow, for any group G, which does not admit a characteristic measure. We construct for every countable group G such a minimal flow. Along the way, we are motivated to consider a family of questions we refer to as minimal subdynamics: Given a countable group G and a collection of infinite subgroups

$\{\Delta _i: i\in I\}$

, when is there a faithful G-flow for which every

$\Delta _i$

acts minimally?

查看原文本刊更多论文

无特征措施的最小亚动力学和最小流动

给定一个可数群 G 和一个 G 流 X，如果 X 上的概率度量 $\mu $ 是 $\mathrm {Aut}(X, G)$ -不变的，那么它就叫做特征度量。弗里施和塔穆兹提出了一个问题：对于任何群 G，是否存在一个最小的 G 流，它不允许特征度量？我们为每个可数群 G 构建了这样一个最小流。在此过程中，我们考虑了一系列我们称之为最小子动力学的问题：给定一个可数群 G 和一个无限子群的集合 $\{\Delta _i: i\in I\}$ ，什么时候存在一个忠实的 G 流，其中每个 $\Delta _i$ 的作用都是最小的？

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

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.