Browsing by Author "Gómez Ortiz, Jaime Andrés"

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    Almost 1-1 extensions, equicontinuous systems and residually finite groups
    (2024) Gómez Ortiz, Jaime Andrés; Cortéz, María Isabel; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
    The purpose of this document is to present our study on the various properties of almost 1-1 extensions of G-odometers with regards to the realization of Choquet simplices, mean-equicontinuity, and the construction of specific almost 1-1 exten- sions of equicontinuous systems. These systems can be viewed as a topological generalization of equicontinuous systems with diverse behavior on some aspects as entropy, the set of probability invariant measures, and more. Each problem is addressed within a general framework without assuming any amenable property on the acting group, except for the last problem where amenability was essential for constructing a specific type of almost 1-1 extensions. This thesis is divided into three parts, with the first two chapters presenting the results of two different manuscripts that are published and submitted, respectively.