KAM techniques in PDE
Séminaire Bourbaki : volume 2001/2002, exposés 894-908, Astérisque no. 290  (2003), Talk no. 908, p. 307-317
@incollection{SB_2001-2002__44__307_0,
     author = {P\'erez-Marco, Ricardo},
     title = {KAM techniques in PDE},
     booktitle = {S\'eminaire Bourbaki : volume 2001/2002, expos\'es 894-908},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {290},
     year = {2003},
     note = {talk:908},
     pages = {307-317},
     zbl = {1064.37058},
     mrnumber = {2074062},
     language = {en},
     url = {http://www.numdam.org/item/SB_2001-2002__44__307_0}
}
Pérez-Marco, Ricardo. KAM techniques in PDE, in Séminaire Bourbaki : volume 2001/2002, exposés 894-908, Astérisque, no. 290 (2003), Talk no. 908, pp. 307-317. http://www.numdam.org/item/SB_2001-2002__44__307_0/

[ARN] V. I. Arnold - Proof of a theorem of A.N. Kolmogorov on the conservation of quasi-periodic motions under a small change of the Hamiltonian function, Uspekhi Mat. Nauk. 18 (1963), no. 5, p. 13-40, Russ. Math. Surv. 18 (1963), no. 5, p. 9-36. | MR 163025 | Zbl 0129.16606

[BOS] J.-B. Bost - Tores invariants des systèmes dynamiques hamiltoniens (d'après Kolmogorov, Arnold, Moser, Rüssmann, Zehnder, Herman, Pöschel, ...), in Sém. Bourbaki 1984-85, Astérisque, vol. 133-134, Soc. Math. France, Paris, 1985, exp. n° 639, p. 113-157. | Numdam | MR 837218 | Zbl 0602.58021

[BOU1] J. Bourgain - Construction of quasi-periodic solutions of Hamiltonian perturbations of linear equations and applications to nonlinear PDE, International Math. Res. Notices 11 (1994), p. 475-497. | MR 1316975 | Zbl 0817.35102

[BOU2] _, Non-linear Schrödinger equations, Park City Lectures, July 1995.

[BOU3] _, On Melnikov's persistence problem, Mathematical Research Letters 4 (1997), p. 445-458.

[BOU4] _, Quasi-periodic solutions of Hamiltonian perturbations of 2D-linear Schrödinger equations, Ann. Math. 148 (1998), p. 363-439. | MR 1668547 | Zbl 0928.35161

[BOU5] _, Green's function estimates for lattice Schrödinger operators and applications, Manuscript, 2001.

[B-G-S] J. Bourgain, M. Goldstein & W. Schlag - Anderson localization for Schrödinger operators on Z2 with quasi-periodic potential, Preprint, 2000. | MR 1947458

[CHE] C.-Q. Chen - Lower dimensional invariant tori in the region of instability for nearly integrable Hamiltonian systems, Comm. Math. Phys. 203 (1999), no. 2, p. 385-419. | MR 1697603 | Zbl 0935.70013

[CRA] W. Craig - Problèmes de petits diviseurs dans les équations aux dérivées partielles, Panoramas et Synthèses, vol. 9, Soc. Math. France, Paris, 2000. | MR 1804420 | Zbl 0977.35014

[C-W] W. Craig & C. E. Wayne - Newton's method and periodic solutions of non-linear wave equations, Comm. Pure Appl. Math. 46 (1993), p. 1409- 1498. | MR 1239318 | Zbl 0794.35104

[ELI1] L. H. Eliasson - Perturbations of stable invariant tori for Hamiltonian systems, Ann. Sco. Norm. Sup. Pisa, Sci. Fis. Mat., Ser. IV XV (1988), no. 1, p. 115-147. | Numdam | MR 1001032 | Zbl 0685.58024

[ELI2] _, Biasymptotic solutions of perturbed integrable Hamiltonian systems, Bol. Soc. Mat. Bras. 25 (1994), no. 1, p. 57-76. | MR 1274762 | Zbl 0799.58026

[GRA] S. M. Graff - On the continuation of hyperbolic invariant tori for Hamiltonian systems, J. Diff. Eq. 15 (1974), p. 1-69. | MR 365626 | Zbl 0257.34048

[K-P] T. Kappeler & J. Pöschel - KDV and KAM, Book to appear in Springer-Verlag. | MR 1997070

[KOL] A. N. Kolmogorov - On the conservation of conditionally periodic motions for a small change in Hamilton's function, Dokl. Acad. Nauk. SSSR 98 (1954), p. 525-530. | MR 68687 | Zbl 0056.31502

[KUK1] S. V. Kuksin - Nearly integrable infinite-dimensional systems, LNM, vol. 1556, Springer-Verlag, 1991.

[KUK2] _, Elements of a qualitative theory of Hamiltonian PDEs, in Proceedings ICM, Vol. II, Berlin (1998), Doc. Math., Deutsche Math. Verein., 1998, p. 819-829. | MR 1648129

[KUK3] _, Analysis of Hamiltonian PDEs, Oxford Lecture Series, vol. 19, Oxford University Press, 2000. | MR 1857574

[LIA] A. M. Liapounov - Problème général de la stabilité du mouvement, Ann. Math. Studies, vol. 17, Princeton Univ. Press, Princeton, 1947. | MR 21186 | Zbl 0031.18403

[MEL] V. K. Melnikov - Dokl. Akad. Nauk. SSSR 165 (1965), no. 6, p. 1245-1248, Dokl. Akad. Nauk. SSSR 181 (1968) no. 3, p. 546-549. | MR 201753

[MOS] J. Moser - Stable and random motions in dynamical systems, Ann. Math. Studies, vol. 77, Princeton Univ. Press, Princeton, 1973. | MR 442980 | Zbl 0271.70009

[NEU1] O. Neugebauer - Astronomical cuneiform texts I, II, III, Springer-Verlag, 1983. | MR 704658

[NEU2] _, The exact sciences in antiquity, Dover Publications, 1969. | MR 260517

[POS1] J. Pöschel - On elliptic lower dimensional tori in Hamiltonian systems, Math. Z. 202 (1989), p. 559-608. | MR 1022821 | Zbl 0662.58037

[POS2] _, Non-linear partial differential equations, Birkhoff normal forms, and KAM theory, in European Congress of Mathematics, Vol. II (Budapest 1996), Progr. Math., vol. 169, Birkhäuser, Basel, 1998.

[PTO] Ptolomy - Almagest, ....

[RUS] H. Russmann - Invariant tori in non-degenerate nearly integrable hamiltonian systems, Regular and Chaotic Dynamics 6 (2001), no. 2, p. 119-204. | MR 1843664 | Zbl 0992.37050

[S-M] C. L. Siegel & J. Moser - Lectures on Celestial Mechanics, Springer-Verlag, 1971. | MR 502448 | Zbl 0817.70001

[YOU] J. You - Perturbations of lower-dimensional tori for Hamiltonian systems, J. Diff. Equ. 152 (1999), no. 1, p. 1-29. | MR 1672008 | Zbl 0919.58055

[ZEH] E. Zehnder - Generalized implicit function theorem with applications to some small divisors problems, I and II, Comm. Pure Appl. Math. 28 (1975), p. 91-140; (1976), p. 49-111. | MR 380867 | Zbl 0309.58006