Index theory for symplectic matrix paths and periodic solutions of Hamiltonian systems with prescribed energy

CDSNS Colloquium
Wednesday, March 2, 2016 - 1:00pm
1 hour (actually 50 minutes)
Skiles 006
Nankai University
One of the major tools in the study of periodic solutions of  Hamiltonian systems is the Maslov-type index theory for symplectic  matrix paths. In this lecture, I shall give first a brief introduction  on the Maslov-type index theory for symplectic matrix paths as well as  the iteration theory of this index. As an application of these  theories I shall give a brief survey about the existence, multiplicity  and stability problems on periodic solution orbits of Hamiltonian  systems with prescribed energy, especially those obtained in recent  years. I shall also briefly explain some ideas in these studies, and  propose some open problems.