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UBC Theses and Dissertations

Structure and randomness in dynamical systems : different forms of equicontinuity and sensitivity García-Ramos, Felipe


We study topological and measure theoretic forms of mean equicontinuity and mean sensitivity for dynamical systems. With this we characterize well known notions like systems with discrete spectrum, almost periodic functions, and subshifts with regular extensions. We also study the limit behaviour of µ-equicontinuous cellular automata. In this thesis we prove a conjecture from [55] (see Corollary 2.3.18); this was indepently solved by Li-Tu-Ye in [45]. In Chapter 3 we answer questions from [8].

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