@article {Berti2011741,
	title = {Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs},
	journal = {Communications in Mathematical Physics},
	volume = {305},
	number = {3},
	year = {2011},
	note = {cited By (since 1996)8},
	pages = {741-796},
	abstract = {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, close to an elliptic equilibrium, we show the existence of Cantor manifolds of elliptic tori which are "branching" points of other Cantor manifolds of higher dimensional tori. We also answer to a conjecture of Bourgain, proving the existence of invariant elliptic tori with tangential frequency along a pre-assigned direction. The proofs are based on an improved KAM theorem. Its main advantages are an explicit characterization of the Cantor set of parameters and weaker smallness conditions on the perturbation. We apply these results to the nonlinear wave equation. {\textcopyright} 2011 Springer-Verlag.},
	issn = {00103616},
	doi = {10.1007/s00220-011-1264-3},
	author = {Massimiliano Berti and Luca Biasco}
}
@article {2006,
	title = {A Birkhoff-Lewis-Type Theorem for Some Hamiltonian PDEs},
	journal = {SIAM J. Math. Anal. 37 (2006) 83-102},
	number = {arXiv.org;math/0310182v1},
	year = {2006},
	abstract = {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 origin. Such periodic orbits bifurcate from resonant finite dimensional invariant tori of the fourth order normal form of the system. Besides standard nonresonance and nondegeneracy assumptions, our main result is obtained assuming a regularizing property of the nonlinearity. We apply our main theorem to a semilinear beam equation and to a nonlinear Schr\\\\\\\"odinger equation with smoothing nonlinearity.},
	doi = {10.1137/S0036141003436107},
	url = {http://hdl.handle.net/1963/2159},
	author = {Dario Bambusi and Massimiliano Berti}
}
@article {2004,
	title = {Bifurcation of free vibrations for completely resonant wave equations},
	journal = {Boll. Unione Mat. Ital. Sez. B 7 (2004) 519-528},
	number = {SISSA;27/2004/M},
	year = {2004},
	abstract = {We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.},
	url = {http://hdl.handle.net/1963/2245},
	author = {Massimiliano Berti and Philippe Bolle}
}
