KAM techniques in PDE
Séminaire Bourbaki : volume 2001/2002, exposés 894-908, Astérisque, no. 290 (2003), Talk no. 908, 11 p.
@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},
     series = {Ast\'erisque},
     note = {talk:908},
     pages = {307--317},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {290},
     year = {2003},
     mrnumber = {2074062},
     zbl = {1064.37058},
     language = {en},
     url = {http://archive.numdam.org/item/SB_2001-2002__44__307_0/}
}
TY  - CHAP
AU  - Pérez-Marco, Ricardo
TI  - KAM techniques in PDE
BT  - Séminaire Bourbaki : volume 2001/2002, exposés 894-908
AU  - Collectif
T3  - Astérisque
N1  - talk:908
PY  - 2003
SP  - 307
EP  - 317
IS  - 290
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/SB_2001-2002__44__307_0/
LA  - en
ID  - SB_2001-2002__44__307_0
ER  - 
%0 Book Section
%A Pérez-Marco, Ricardo
%T KAM techniques in PDE
%B Séminaire Bourbaki : volume 2001/2002, exposés 894-908
%A Collectif
%S Astérisque
%Z talk:908
%D 2003
%P 307-317
%N 290
%I Société mathématique de France
%U http://archive.numdam.org/item/SB_2001-2002__44__307_0/
%G en
%F 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, 11 p. http://archive.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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

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

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

[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 | Zbl

[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

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

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

[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

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

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

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

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

[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 | Zbl

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

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

[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 | Zbl