Asymmetry in Dynamics

Explore the concept of asymmetry in dynamical systems through this 45-minute distinguished lecture by Amie Wilkinson from the University of Chicago. Delve into the meaning of symmetries in various dynamical contexts, including complex analytic, Hamiltonian, and smooth systems. Examine progress towards resolving Smale's conjecture that generic smooth dynamical systems possess only trivial symmetries. Learn about dynamical symmetries, their role in mapping orbits, and how they preserve asymptotic dynamical invariants and Julia sets. Investigate smooth flows, their symmetries, and Hamiltonian dynamics, including Hamilton's equations. Gain insights into this complex topic through a comprehensive exploration of symmetry and asymmetry in dynamics.

Intro
What is symmetry?
What is a dynamical symmetry?
Symmetries map orbits to orbits
Symmetries preserve asymptotic dynamical invariants
Example: symmetries preserve Julia sets
Smooth flows and their symmetries
Hamiltonian dynamics
Hamilton's equations
Smale's question