When Topology Forces Dynamics - Lecture 2

Explore the intersection of topology and dynamics in this lecture on "When topology forces dynamics." Delve into how topological considerations, such as actions on homology or the fundamental group, can reveal significant insights about a system's dynamics. Examine the concept of dynamics preserved under large perturbations within the same homotopy class. Investigate model systems with well-understood but complex dynamics, and learn how their dynamics are maintained under homotopy. Understand the crucial role of hyperbolicity at various scales in these theorems. Cover key topics including the fixed point index, Lefschetz formula, Nielsen Theory, Franks and Handel homotopy stability theorems, and pseudoAnosov maps. Discover applications to the partial order on braid types, rotation sets, and fluid mixing in this comprehensive 1-hour and 28-minute lecture by Philip Boyland from the University of Florida, part of the Simons Semester on Dynamics series.