— We present recent existence results of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on T , db 1, finitely di¤erentiable nonlinearities, and tangential… (More)

We prove the existence of small amplitude periodic solutions, with strongly irrational frequency ω close to one, for completely resonant nonlinear wave equations. We provide multiplicity results for… (More)

We consider infinite dimensional Hamiltonian systems. We prove the existence of “Cantor manifolds” of elliptic tori–of any finite higher dimension–accumulating on a given elliptic KAM torus. Then,… (More)

In this paper we give an extension of the Birkhoff–Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the… (More)

We prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with… (More)

We present a new method for the automatic classification of Persistent Scatters Interferometry (PSI) time series based on a conditional sequence of statistical tests. Time series are classified into… (More)

We prove bifurcation of Cantor families of periodic solutions for wave equations with nonlinearities of class C. It requires a modified Nash-Moser iteration scheme with interpolation estimates for… (More)

We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations.… (More)

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing… (More)

We prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs.… (More)