Wouter Jongeneel: Homotopy questions and stability of dynamical systems

Abstract.

Motivated by the field of automatic control, in this talk we discuss the following two questions: (i) Are dynamical systems that render a set asymptotically stable, homotopic through dynamical systems that preserve this notion of stability? (ii) When is a closed attractor, on a metric space, homotopy equivalent to its basin of attraction? These questions are addressed using tools from differential and algebraic topology, respectively. This work builds in particular upon results by Auslander, Bhatia and Wilson. We aim to be visual and make the talk accessible to a large audience.