Mathematics

The plan of the course is to study the complex dynamics of the NLS equation on T^2, focusing on both chaotic and regular behavior.
The first part of the course will be dedicated to an overview of Birkhof normal form and reducibility results for vector fields on
scales of Hilbert spaces.  Then we shall discuss the existence  of  Cantor families of quasi-periodic solutions, both  linearly stable and unastable.
Finally, close to such very regular solutions, we shall exhibit "diffusive'' solutions whose Sobolev norm increases by an arbitrarily large factor.

The course "Nonlinear Schrodinger equation on T^d will continue concerning lower bounds on the growth of the Sobolev norms of a solution.