Richard de Beer, Rocco Duvenhage, Anton Stroh
We extend previous results on noncommutative recurrence in unital *-algebras over the integers, to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine's recurrence theorem, as well as a form of multiple recurrence. This is done using the mean ergodic theorem in Hilbert space, via the GNS construction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Estimating the Hausdorff measure by recurrence
本文提出一种通过计算点自身最近回归时间来从下方估计分形集豪斯多夫测度的新方法。
In this article, we consider hyperbolic rational maps restricted on thier Julia sets and study about the recurrence rate of typical orbits in arbitrarily small neighbourhoods around them and their relationship to the Hausdorff dimension of such small neighbourhoods.
We consider linear mappings on the $d$-dimensional torus, defined by $T(x) = Ax \pmod 1$, where $A$ is an invertible $d \times d$ integer matrix, with no eigenvalues on the unit circle. In the case $d = 2$ and $\det A = \pm 1$, we give a formula for the Hausdorff dimension of the set \[ \{ \, x \in \mathbb{T}^d : d (T^n (x), x) < e^{- αn} \text{ for infinitely many } n \, \}. \]
By employing the recurrence method worked out in `Estimating the Hausdorff measure by recurrence', we provide effective lower estimates of the proper--dimensional Hausdorff measure of minimal sets of circle homeomorphisms that are not conjugate to any rotation.
Shrinking targets versus recurrence: A survey on the Hausdorff dimension theory
该综述对比动力系统中收缩目标集与回归集的豪斯多夫维数，涉及多类动力系统，还涵盖相关测度结果及坏逼近轨道等内容。
Quantitative recurrence problem on some Bedford-McMullen carpets
针对 Hausdorff 维数与盒维数相等的 Bedford-McMullen 地毯，论文研究其典范自同态定量回归集的 Hausdorff 维数。
Hausdorff dimension of recurrence sets for matrix transformations of tori
本文研究环面上由整数矩阵诱导的变换的回归集的豪斯多夫维数，在矩阵可对角化且特征值为整数时给出了维数公式。
Intersections of quantitative recurrence and badly approximable sets for expanding Markov maps
针对单位区间上含 sofic β-变换等的扩张马尔可夫映射，研究动态 badly approximable 点的定量回归性质，确定回归集与 badly approximable 集等交集的豪斯多夫维数，得到相关结果。
Hausdorff dimension of the set of eventually always hitting points on a self-conformal set
本文在自共形迭代函数系统框架下研究最终总是命中集与收缩目标集之交的豪斯多夫维数，给出其上界和下界，并得到两者交集的维数结果。
The recurrence spectrum for dynamical systems beyond specification
本文提出（W'）-规范概念，证明了特定子移位的复发集具有满豪斯多夫维度，并扩展到广泛类别的分段扩张区间映射。
For a given rotation number we compute the Hausdorff dimension of the set of well approximable numbers. We use this result and an inhomogeneous version of Jarnik's theorem to show strong recurrence properties of the billiard flow in certain polygons
We explore the problem of finding the Hausdorff dimension of the set of points that recur to shrinking targets on a self-affine fractal. To be exact, we study the dimension of a certain related symbolic recurrence set. In many cases this set is equivalent to the recurring set on the fractal.
Return time sets and product recurrence
该研究探讨了在紧Hausdorff空间中，群作用下子集包含返回时间集的条件，并通过积递归与distality的关系回答了相关问题。
Let $π\colon T\times X\rightarrow X$ with phase map $(t,x)\mapsto tx$, denoted $(π,T,X)$, be a \textit{semiflow} on a compact Hausdorff space $X$ with phase semigroup $T$. If each $t\in T$ is onto, $(π,T,X)$ is called surjective; and if each $t\in T$ is 1-1 onto $(π,T,X)$ is called invertible and in latter case it induces $π^{-1}\colon X\times T\rightarrow X$ by $(x,t)\mapsto xt:=t^{-1}x$, denoted $(π^{-1},X,T)$. In this paper, we show that $(π,T,X)$ is equicontinuous surjective iff it is uniformly distal iff $(π^{-1},X,T)$ is equicontinuous surjective. As applications of this theorem, we also…
Let $X$ be a zero-dimensional locally compact Hausdorff space not necessarily metric and $G$ a compactly generated topological group not necessarily abelian or countable. We define recurrence at a point for any continuous action of $G$ on $X$, and then, show that if $\overline{Gx}$ is compact for all $x\in X$, the conditions (i) this dynamics is pointwise recurrent, (ii) $X$ is a union of $G$-minimal sets, (iii) the $G$-orbit closure relation is closed in $X\times X$, and (iv) $X\ni x\mapsto \overline{Gx}\in 2^X$ is continuous, are pairwise equivalent. Consequently, if this dynamics is distal,…
We define recurrence for a compactly generated para-topological group $G$ acting continuously on a locally compact Hausdorff space $X$ with $\dim X=0$, and then, show that if $\overline{Gx}$ is compact for all $x\in X$, the conditions (i) this dynamics is pointwise recurrent, (ii) $X$ is a union of $G$-minimal sets, (iii) the $G$-orbit closure relation is closed in $X\times X$, and (iv) $X\ni x\mapsto \overline{Gx}\in 2^X$ is continuous, are pairwise equivalent. Consequently, if this dynamics is pointwise product recurrent, then it is pointwise regularly almost periodic and equicontinuous; mor…
A noncommutative transfer principle
该文将广义Calderon转移原理推广至非交换框架，通过构造转移算子及双变量递减重排与极大算子工具，为半有限冯·诺依曼代数上的群作用建立遍历收敛结果。
We introduce and systematically study the notion of Rokhlin dimension (with and without commuting towers) for compact group actions on $C^*$-algebras. This notion generalizes the one introduced by Hirshberg, Winter and Zacharias for finite groups, and contains the Rokhlin property as the zero dimensional case. We show, by means of an example, that commuting towers cannot always be arranged, even in the absence of $K$-theoretic obstructions. For a compact Lie group action on a compact Hausdorff space, freeness is equivalent to finite Rokhlin dimension of the induced action. We compare the notio…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。