Abstract:
This is a joint work with Amadeu Delshams and Piotr Zgliczcynski.

The main goal of our work is to understand the geometric mechanism that
gives rise the instability shown by Colliander et al (2010) in the
Nonlinear Schrodinger Equation with cubic defocusing. It can be seen as a
diffusion mechanism, but it appears that the geometric skeleton of the
system is not the standard for Arnold Diffusion: instead of having a
sequence of non-resonant invariant tori connected along transverse
heteroclinic orbits we have a non-transversal situation.

We expose that the instability (diffusion) can be achieved due to the large
dimension of the system, while we try to generate a scheme for this new
kind of diffusion that could be applied to other infinitely dimensional
Hamiltonian systems.