TY - JOUR
T1 - Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs
JF - Communications in Mathematical Physics
Y1 - 2011
A1 - Massimiliano Berti
A1 - Luca Biasco
AB - 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. © 2011 Springer-Verlag.
VL - 305
N1 - cited By (since 1996)8
ER -