Enrico VALDINOCI

Piazza Enrico Fermi 37
00146 Roma
Italy
valdino@ciop.mat.uniroma3.it

Whiskered tori for "a priori" stable and unstable Hamiltonian systems

Abstract: We revisited one of the results of Chierchia and Gallavotti's "Drifts and diffusion in phase space", 1994, and gave a detailed statement for a KAM theorem about the conservation of partially hyperbolic tori on a fixed energy level. In particular, we emphasized the following items: sharp estimates on the measures of the surviving tori on the energy level, an elementary proof of smooth embedding (without making use of the Whitney Extension Theorem) and Cinfinity-closeness to identify of the transformations involved, analyticity properties (including dependence upon parameters), geometric structures. These results apply to both "a priori unstable" and "a priori stable" systems.