References
D. Bambusi,Long time stability of some small amplitude solutions in nonlinear Schrödinger equations, Comm. Math. Phys.189 (1997), 205–226.
D. Bambusi,Nekhoroshev theorem for small amplitude solutions in nonlinear Schrödinger equations, Math. Z.230 (1999), 345–387.
J. Bourgain,Nonlinear Schrödinger Equations, Park City Lectures, Amer. Math. Soc, Providence, 1999.
J. Bourgain,Global Solutions of Nonlinear Schrödinger Equations, Amer. Math. Soc. Colloq. Publ.46 (1999).
J. Bourgain,On the growth in time of higher Sobolev norms of smooth solutions of Hamiltonian PDE, Internat. Math. Res. Notices No. 6, (1996), 277–304.
J. Bourgain,Construction of approximative and almost periodic solutions of perturbed linear Schrödinger and wave equations, Geom. Funct. Anal.6 (1996), 201–230.
G. Benettin, J. Fröhlich and A. Giorgili,A Nekhoroshev-type theorem for Hamiltonian systems with infinitely many degrees of freedom, Comm. Math. Phys.119 (1989), 95–108.
L. Cmerchia,On the stability problem for nearly-integrable Hamiltonian systems, inSeminar on Dynamical Systems, Progress in Nonlinear Differential Equations, BirkhÄuser, Boston, 1997, pp. 35–46.
W. Craig,Problèmes de petits diviseurs dans les équations aux dérivées partielles, preprint.
S. Kuksin, Private communication.
S. Kuksin and J. Pöschel,Invariant Cantor manifolds of quasi-periodic oscillations for a nonlinear Schrödinger equation, Ann. of Math. (2)143 (1996), 149–179.
P. Lochak,Canonical perturbation theory via simultaneous approximation, Uspekhi Mat. Nauk47 (6) (1992) 59–140.
N. Nekhoroshev,An exponential estimate of the time of stability of nearly integrable Hamiltonian systems, Uspekhi Mat. Nauk32 (1) (1977), 5–66
G. Staffilani,Quadratic forms for a 2D semilinear Schrödinger equation, Duke Math. J.86 (1997), 79–108.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially supported by NSF grant DMS-9801013.
Rights and permissions
About this article
Cite this article
Bourgain, J. On diffusion in high-dimensional Hamiltonian systems and PDE. J. Anal. Math. 80, 1–35 (2000). https://doi.org/10.1007/BF02791532
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02791532