Abstract
Abstract In this paper, in both topological and measure-theoretical senses, various types of sequence equicontinuity and bounded sequence complexity via Furstenberg family are introduced, and the interrelationships among which and rigidity are systematically studied, which generalize many known results in the literature. In particular, it is shown that a topological dynamical system (X, T) is uniformly rigid iff it is F r -equicontinuous of type 4 iff it has bounded F r -complexity of type 4; And a measure-preserving system ( X , B X , μ , T ) is rigid iff it is µ- F r -mean equicontinuous of type 4 iff it has bounded µ- F r -mean complexity of type 4, where F r is the Furstenberg family consisting of all sequences like q N ( q ∈ N ). Moreover, several examples are also constructed to distinguish the new notions or illustrate the scopes of some conclusions, while concurrently addressing a few questions posed in earlier articles.
Published Version
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