This course explores the concepts of symmetry and asymmetry in dynamics, focusing on dynamical symmetry groups, Hamiltonian dynamics, and the preservation of dynamical invariants. The course teaches about Noether's Theorem, Smale's conjecture, and Kopell's Theorem. The teaching method involves lectures and examples to illustrate how symmetries map orbits and preserve asymptotic dynamical invariants. This course is intended for individuals interested in advanced topics in mathematics and dynamics.
Overview
Syllabus
Intro
What is symmetry?
What is a dynamical symmetry?
The dynamical symmetry group (f)
Symmetries map orbits to orbits
Symmetries preserve asymptotic dynamical invariants
Example: symmetries preserve Julia sets
Smooth flows and their symmetries
Theme: symmetries are special
Hamiltonian dynamics
Noether's Theorem (1915)
Smale's conjecture
Kopell's Theorem (1970)
Symmetry rigidity: project with D. Damjanović and D. Xu
Taught by
Joint Mathematics Meetings
