March 4, 2005: Samuel Lisi, CIMS
Hunting for Homoclinic orbits (with a geometric PDE)
A Hamiltonian system is a special kind of ODE, classically used to model a
physical system in which energy is conserved. One of the big questions is
to understand what special orbits can occur and how many of them there are 
examples of special orbits include periodic orbits and homoclinic orbits.
Until the mid80's, most of the advances in the field came by studying a
variational problem. Then, Floer turned the field on its head by studying a
firstorder elliptic PDE and using this to relate periodic orbits of the
Hamiltonian system to certain geometric properties.
I will present a quick overview of the successes achieved by this means and
will then show how the existing theory can be extended to prove the existence
of a homoclinic orbit in certain special circumstances.
The talk will not assume any significant geometry background. Instead, the
primary emphasis will be on the PDE methods and problems that arise.
