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Explore the fundamentals of local entropy theory in dynamical systems through this lecture that delves into topological and combinatorial descriptions of entropy occurrence. Learn how this mathematical framework can be applied to prove diverse results, including the identification of homoclinic points in algebraic actions and understanding the descriptive complexity of dynamical systems with completely positive entropy. Gain insights into the theoretical foundations that bridge the connection between entropy theory and seemingly unrelated mathematical concepts, presented as part of the Simons Semester on Dynamics series.
