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Explore the intersection of topology and dynamics in this lecture titled "When topology forces dynamics." Delve into scenarios where topological considerations, such as actions on homology or the fundamental group, significantly influence a system's dynamics. Examine the preservation of dynamics under large perturbations within the same homotopy class. Investigate model systems with well-understood yet complex dynamics, and learn how their characteristics persist through homotopy. Understand the crucial role of hyperbolicity at various scales in these phenomena. Cover key topics including the fixed point index, Lefschetz formula, Nielsen Theory, Franks and Handel homotopy stability theorems, pseudoAnosov maps, and their applications to the partial order on braid types, rotation sets, and fluid mixing.
