Walter Craig

Invariant tori for Hamiltonian PDE


 
Abstract:
The course will address questions on the existence of KAM tori in Hamiltonian PDE, with the point of view being to address problems of exact resonance, as well as classical small divisors.

 
1. Hamiltonian partial differential equations and Hamiltonian systems with infinitely many degrees of freedom.
2. The Lyapunov center theorem and the resonant theorems of A. Weinstein and J. Moser.
3. The Nash Moser method in this setting.
4. The linearized problem: resolvant estimates of J. Froehlich. T. Spencer and J. Bourgain.
5. Construction of Cantor varieties of invariant tori.