A Simple Proof of the Conley Conjecture for Hamiltonian Diffeomorphisms C^1-Close to the Identity

Working Group on Symplectic Dynamics
Topic:A Simple Proof of the Conley Conjecture for Hamiltonian Diffeomorphisms C^1-Close to the Identity
Speaker:Marco Mazzucchelli
Affiliation:Pennsylvania State University
Date:Wednesday, February 29
Time/Room:4:00pm - 5:00pm/S-101

The Conley conjecture, recently established by Nancy Hingston, asserts that every Hamiltonian diffeomorphism of a standard symplectic 2n-torus admits infinitely many periodic points. While this conjecture has been extended to more general closed symplectic manifolds, all the known proofs require sophisticated arguments. In this talk, we use generating function techniques in symplectic geometry to give a simple proof of the conjecture for those Hamiltonian diffeomorphisms of the torus that are C^1-close to the identity.