01306nas a2200145   4500008004100000022001300041245007600054210006900130300001200199490000800211520079500219100002401014700001701038856010501055       2011                        eng d  a0010361600aBranching of Cantor Manifolds of Elliptic Tori and Applications to PDEs0 aBranching of Cantor Manifolds of Elliptic Tori and Applications   a741-7960 v3053 aWe 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.1 aBerti, Massimiliano1 aBiasco, Luca  uhttps://www.math.sissa.it/publication/branching-cantor-manifolds-elliptic-tori-and-applications-pdes