In 1978, Charles Conley classified all continuous dynamical systems. His theorem, dubbed the "fundamental theorem of dynamical systems" states that the orbits of any continuous map on a compact metric space fall into two classes: gradient-like and recurrent. When the recurrent part is factored out, the dynamics appear to be gradient-like. While one might wonder how a theorem that applies to every continuous map could be of any use, it plays a foundational role in many deep results.
Conley's fundamental theorem of dynamical systems
University of Chicago
Date & Time
May 20, 2020 | 5:30 – 7:00pm
Remote Access Only