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}
}
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… 
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