January 21, 2025
Title: Robustness of Topological Entropy for Geodesic Flows (MI talk)
Speaker: Lucas Dahinden
Topological entropy (=h) is a numerical invariant of maps that measures chaotic behaviour. It is well known, that h is not lower semi-continuous: There are examples where smooth perturbations lead to total collapse of h. However, sometimes a geometric feature prevents this collapse. In this talk we explore some of these features and discuss their consequences: On the 2-torus we investigate contractible closed geodesics, an intersection pattern that we call "ribbon" and on general manifolds we investigate a feature that we call "retractable neck".
This is joint work with Marcelo Alves, Matthias Meiwes and Louis Merlin.