Overview
This course aims to explore the concept of asymmetry in dynamics, focusing on the absence of non-trivial symmetries in generic smooth dynamical systems. The course covers topics such as the definition of symmetry in various types of dynamical systems, the preservation of dynamical invariants by symmetries, and the implications of symmetries on Julia sets. The teaching method involves lectures and discussions led by the instructor. This course is intended for individuals interested in advanced topics in dynamical systems and mathematics.
Syllabus
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
Taught by
International Centre for Theoretical Sciences