Multiple recurrence theorems for set-valued maps
type: Item
instance of: scholarly article
title: Multiple recurrence theorems for set-valued maps
zbMATH Open document ID: 1377.37011
author: Shu-Qi Huang
author: Hailan Liang
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-08-03T00:00:00Z
review text: In [Compos. Math. 1, 177--179 (1934; JFM 60.0359.01)] \textit{A. Khintchine} strengthened the Poincaré recurrence theorem, showing that if \(T\) is a measure-preserving transformation of a probability space \((X,{\mathcal {B}},\mu)\) and if \(A\in {\mathcal {B}}\) with \(\mu (A) > 0\), then for every \(\varepsilon > 0\), the set \( \{n\in {\mathbb {N}}: \mu (A \cap T^{-n}(A)) > \mu (A)^2 - \varepsilon\}\) is syndetic. In this paper the authors extend the Khinchine's recurrence theorem, the Furstenberg's multiple recurrence theorem, and the multiple Birkhoff recurrence theorem from single valued maps to set-valued maps.
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 37B20
zbMATH DE Number: 6756245
zbMATH Keywords: multiple recurrence theorem
zbMATH Keywords: set-valued map
reviewed by: Bolis Basit
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.06.008
OpenAlex ID: W2624480000
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DOI: 10.1016/J.JMAA.2017.06.008
description: scientific article; zbMATH DE number 6756245