A characterization theorem showing that for adequate integer sequences, a subgroup condition exactly determines when a unitary operator or measure-preserving transformation can be rigid along some given subsequences and mixing along others.
Rigidity and Non-recurrence along Sequences
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abstract
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main focus in this article is to characterize explicitly the structural properties of sequences which can be rigidity sequences or non-recurrent sequences for some weakly mixing dynamical system. For ergodic transformations generally and for weakly mixing transformations in particular there are both parallels and distinctions between the class of rigid sequences and the class of non-recurrent sequences. A variety of classes of sequences with various properties are considered showing the complicated and rich structure of rigid and non-recurrent sequences.
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math.DS 1years
2025 1verdicts
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Coexistence of mixing and rigid behaviors in ergodic theory
A characterization theorem showing that for adequate integer sequences, a subgroup condition exactly determines when a unitary operator or measure-preserving transformation can be rigid along some given subsequences and mixing along others.