@article {Bambusi20113379,
title = {Degenerate KAM theory for partial differential equations},
journal = {Journal of Differential Equations},
volume = {250},
number = {8},
year = {2011},
note = {cited By (since 1996)3},
pages = {3379-3397},
abstract = {This paper deals with degenerate KAM theory for lower dimensional elliptic tori of infinite dimensional Hamiltonian systems, depending on one parameter only. We assume that the linear frequencies are analytic functions of the parameter, satisfy a weak non-degeneracy condition of R{\"u}ssmann type and an asymptotic behavior. An application to nonlinear wave equations is given. {\textcopyright} 2010 Elsevier Inc.},
issn = {00220396},
doi = {10.1016/j.jde.2010.11.002},
author = {Dario Bambusi and Massimiliano Berti and Elena Magistrelli}
}
@article {2003,
title = {Drift in phase space: a new variational mechanism with optimal diffusion time},
journal = {J. Math. Pures Appl. 82 (2003) 613-664},
number = {arXiv.org;math/0205307v1},
year = {2003},
publisher = {Elsevier},
abstract = {We consider non-isochronous, nearly integrable, a-priori unstable Hamiltonian systems with a (trigonometric polynomial) $O(\\\\mu)$-perturbation which does not preserve the unperturbed tori. We prove the existence of Arnold diffusion with diffusion time $ T_d = O((1/ \\\\mu) \\\\log (1/ \\\\mu))$ by a variational method which does not require the existence of {\textquoteleft}{\textquoteleft}transition chains of tori\\\'\\\' provided by KAM theory. We also prove that our estimate of the diffusion time $T_d $ is optimal as a consequence of a general stability result derived from classical perturbation theory.},
doi = {10.1016/S0021-7824(03)00032-1},
url = {http://hdl.handle.net/1963/3020},
author = {Massimiliano Berti and Luca Biasco and Philippe Bolle}
}
@article {2000,
title = {Diffusion time and splitting of separatrices for nearly integrable},
journal = {Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 2000, 11, 235},
number = {SISSA;90/00/M},
year = {2000},
publisher = {SISSA Library},
url = {http://hdl.handle.net/1963/1547},
author = {Massimiliano Berti and Philippe Bolle}
}