Large time blow up for a perturbation of the cubic Szegő equation

الأصل · EN

We consider the following Hamiltonian equation on a special manifold of rational functions, i_tu=Π(|u|²u)+ (u|1),∈, where Π denotes the Szegő projector on the Hardy space of the circle ¹. The equation with =0 was first introduced by Gérard and Grellier in GG1 as a toy model for totally non dispersive evolution equations. We establish the following properties for this equation. For 0, any compact subset of initial data leads to a relatively compact subset of trajectories. For 0, there exist trajectories on which high Sobolev norms exponentially grow with time.