Measure-theoretic equicontinuity and rigidity. (9th June 2020)

• Record Type: Journal Article
• Authors: Cai, Fangzhou
• Is Part Of: Nonlinearity. Volume 33:Number 8(2020)
• Page Start: 3739
• Page End: 3762
• Publication Date: 2020-06-09
• Subjects: measure-theoretic equicontinuity -- rigidity -- sequence entropy; 37A05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab8a67
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Let ( X, T ) be a topological dynamical system and μ ∈ M ( X, T ). We show that ( X, B, μ, T ) is rigid if and only if there exists some subsequence A of N such that ( X, T ) is μ – A -equicontinuous if and only if there exists some IP-set A such that ( X, T ) is μ – A -equicontinuous. We show that if there exists some subsequence A of N with positive upper density such that ( X, T ) is μ – A -mean-equicontinuous, then ( X, B, μ, T ) is rigid. We also give results with respect to a function.