AN INVERSE OF FURSTENBERG'S CORRESPONDENCE PRINCIPLE AND APPLICATIONS TO NICE RECURRENCE

被引：0

作者：

Fish, Alexander ^{[1
]}

Skinner, Sean ^{[1
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, Australia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2025年

基金：

澳大利亚研究理事会;

关键词：

Sets of recurrence; uniformity in recurrence; Furstenb erg's correspon dence principle; SEQUENCES;

D O I：

10.3934/dcds.2025055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an inverse of Furstenberg's correspondence principle stating that for all measure preserving systems (X, mu, T) and A C X measurable, there exists a set E C N such that mu \k i=1 T-niA = lim N ->infinity N Tk i=1(E - ni) n {0, ..., N - 1} for all positive integers k and all n1, ..., nk E N. As a corollary, we show that a set R C N is a set of nice recurrence if and only if it is nicely intersective. Together, the inverse of Furstenb erg's correspondence principle and its corollary partially answer two questions of Moreira.

引用

页数：11