TY - JOUR
T1 - Degenerate KAM theory for partial differential equations
JF - Journal of Differential Equations
Y1 - 2011
A1 - Dario Bambusi
A1 - Massimiliano Berti
A1 - Elena Magistrelli
AB - 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 Rüssmann type and an asymptotic behavior. An application to nonlinear wave equations is given. © 2010 Elsevier Inc.
VL - 250
N1 - cited By (since 1996)3
ER -
TY - JOUR
T1 - Drift in phase space: a new variational mechanism with optimal diffusion time
JF - J. Math. Pures Appl. 82 (2003) 613-664
Y1 - 2003
A1 - Massimiliano Berti
A1 - Luca Biasco
A1 - Philippe Bolle
AB - 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 ``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.
PB - Elsevier
UR - http://hdl.handle.net/1963/3020
U1 - 1313
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Diffusion time and splitting of separatrices for nearly integrable
JF - Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei Mat. Appl., 2000, 11, 235
Y1 - 2000
A1 - Massimiliano Berti
A1 - Philippe Bolle
PB - SISSA Library
UR - http://hdl.handle.net/1963/1547
U1 - 2571
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -