Syndetic proximality and scrambled sets

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. © 2013 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University.