Contributions to Structure Theory in Topological Dynamics and Ergodic Theory

Abstract

This thesis contributes to the structure theory of dynamical systems across four different areas. Building on the foundational work by Ellis on enveloping semigroups, we introduce "enveloping semigroupoids" to capture relative properties of dynamical systems in algebraic terms. Via a systematic development of the representation theory of these groupoids, we provide a conceptually new perspective on existing structure-theoretic results for minimal dynamical systmes and expand these results to systems with more intricate orbit Show more