From Hamiltonian dynamics to symplectic capacities

Dynamical Systems Working Seminar
Thursday, May 3, 2012 - 16:00
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech.
In this introductory talk, we review the dynamical motivation for definingsymplectic manifolds, then describe a class of invariants called symplecticcapacities, which are closely related to both volume and the existence ofperiodic orbits. We explore the connections and differences between thesethree notions in the context of some basic phenomena/problems in symplecticgeometry: Gromov's nonsqueezing theorem, the difference between symplecticand volume-preserving diffeomorphisms, and the question of existence ofclosed characteristics on energy surfaces.