# Rigidity and non-recurrence along sequences

@article{Bergelson2013RigidityAN,
title={Rigidity and non-recurrence along sequences},
author={Vitaly Bergelson and Andr{\'e}s del Junco and Mariusz Lemanczyk and Joseph M. Rosenblatt},
journal={Ergodic Theory and Dynamical Systems},
year={2013},
volume={34},
pages={1464 - 1502}
}
• Published 4 March 2011
• Mathematics
• Ergodic Theory and Dynamical Systems
Abstract We study two properties of a finite measure-preserving dynamical system and a given sequence $({n}_{m} )$ of positive integers, namely rigidity and non-recurrence. Our goal is to find conditions on the sequence which ensure that it is, or is not, a rigid sequence or a non-recurrent sequence for some weakly mixing system or more generally for some ergodic system. The main focus is on weakly mixing systems. For example, we show that for any integer $a\geq 2$ the sequence ${n}_{m} = {a… Non-recurrence sets for weakly mixing linear dynamical systems • S. Grivaux • Mathematics Ergodic Theory and Dynamical Systems • 2012 Abstract We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Non-ergodic$\mathbb{Z}$-periodic billiards and infinite translation surfaces • Mathematics • 2014 We give a criterion which proves non-ergodicity for certain infinite periodic billiards and directional flows on$\mathbb{Z}$-periodic translation surfaces. Our criterion applies in particular to a Kazhdan constants, continuous probability measures with large Fourier coefficients and rigidity sequences • Mathematics Commentarii Mathematici Helvetici • 2020 Exploiting a construction of rigidity sequences for weakly mixing dynamical systems by Fayad and Thouvenot, we show that for every integers$p_{1},\dots,p_{r}$there exists a continuous probability On modulated ergodic theorems • Mathematics • 2017 Let$T$be a weakly almost periodic (WAP) linear operator on a Banach space$X$. A sequence of scalars$(a_n)_{n\ge 1}${\it modulates}$T$on$Y \subset X$if$\frac1n\sum_{k=1}^n a_kT^k x$Rigidity times for a weakly mixing dynamical system which are not rigidity times for any irrational rotation • Mathematics Ergodic Theory and Dynamical Systems • 2014 We construct an increasing sequence of natural numbers$(m_{n})_{n=1}^{+\infty }$with the property that$(m_{n}{\it\theta}[1])_{n\geq 1}$is dense in$\mathbb{T}$for any${\it\theta}\in
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