动力系统的发散协指数序列

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Topology and Analysis Pub Date : 2021-03-22 DOI:10.1142/s1793525322500042

Ruxi Shi, M. Tsukamoto

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引用次数: 1

摘要

当有限群自由作用于拓扑空间时，我们可以定义它的索引和协索引。它们大致衡量给定动作的大小。我们探讨了该指标理论与拓扑动力学之间的相互作用。给定一个不动点自由动力系统，[公式:见文]-周期点的集合对于每个素数[公式:见文]承认[公式:见文]的自然自由作用。我们感兴趣的是它的指数和协指数的增长[公式:见文本]。我们的主要结果表明存在一个具有发散协指数序列的不动点自由动力系统。本文解决了M. Tsukamoto, M. Tsutaya和M. Yoshinaga提出的问题，[公式:见文本]-索引，拓扑动力学和标记性质，预印本(2020)，arXiv: 2012.15372。

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Divergent coindex sequence for dynamical systems

When a finite group freely acts on a topological space, we can define its index and coindex. They roughly measure the size of the given action. We explore the interaction between this index theory and topological dynamics. Given a fixed-point free dynamical system, the set of [Formula: see text]-periodic points admits a natural free action of [Formula: see text] for each prime number [Formula: see text]. We are interested in the growth of its index and coindex as [Formula: see text]. Our main result shows that there exists a fixed-point free dynamical system having the divergent coindex sequence. This solves a problem posed by M. Tsukamoto, M. Tsutaya and M. Yoshinaga, [Formula: see text]-index, topological dynamics and marker property, preprint (2020), arXiv: 2012.15372.

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来源期刊

Journal of Topology and Analysis MATHEMATICS-

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.