Syndetic proximality and scrambled sets

T. K. Subrahmonian Moothathu, Piotr Oprocha

Abstract


This paper is a systematic study about the syndetically proximal relation and the possible existence of syndetically scrambled sets for the dynamics of continuous self-maps of compact metric spaces. Especially we consider various classes of transitive subshifts, interval maps, and topologically Anosov maps. We also present many constructions and examples.

Keywords


Syndetically proximal; scrambled set; Li-Yorke chaos; entropy; transitivity; subshift; interval map

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