Filippo Giuliani

at UPC
Research area: Dynamical Systems / Partial Differential Equations

PhD in Mathematics obtained at SISSA Trieste (2017)


Research lines

My research interests concern the dynamics of PDEs, mostly Hamiltonian. More precisely I am working on KAM theory for PDEs on compact manifolds, reducibility of quasi-periodically time dependent linear operator, growth of Sobolev norms, Birkhoff normal form methods, Arnold Diffusion for infinite dimensional dynamical systems.

Selected publications

1) Giuliani F., "Quasi-periodic solutions for quasi-linear generalized KdV equations", Journal of Differential Equations (2017);

2) Feola R., Giuliani F., Montalto R., Procesi M., "Reducibility of first order operators on tori via Moser's theorem", Journal of Functional Analysis (2019);

3) Feola R., Giuliani F., Pasquali S., "On the integrability of the Degasperis-Procesi equation: control of Sobolev norms and Birkhoff resonances", Journal of Differential Equations (2018);

4) Feola R., Giuliani F., Procesi M., "Reducibility for a class of weakly dispersive linear operators arising from the Degasperis-Procesi equation", Dynamics of Partial Differential Equations (2019);

5) Feola R., Giuliani F., Procesi M., "Reducible KAM tori for Degasperis-Procesi equation", Arxiv (preprint 2019).