Lindstedt series, ultraviolet divergences and Moser's theorem
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 3, pp. 545-593. 
@article{ASNSP_1998_4_26_3_545_0,
     author = {Bonetto, Federico and Gallavotti, Giovanni and Gentile, Guido and Mastropietro, Vieri},
     title = {Lindstedt series, ultraviolet divergences and {Moser's} theorem},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {545--593},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 26},
     number = {3},
     year = {1998},
     mrnumber = {1635706},
     zbl = {0931.37034},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1998_4_26_3_545_0/}
}
TY  - JOUR
AU  - Bonetto, Federico
AU  - Gallavotti, Giovanni
AU  - Gentile, Guido
AU  - Mastropietro, Vieri
TI  - Lindstedt series, ultraviolet divergences and Moser's theorem
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1998
SP  - 545
EP  - 593
VL  - 26
IS  - 3
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1998_4_26_3_545_0/
LA  - en
ID  - ASNSP_1998_4_26_3_545_0
ER  - 
%0 Journal Article
%A Bonetto, Federico
%A Gallavotti, Giovanni
%A Gentile, Guido
%A Mastropietro, Vieri
%T Lindstedt series, ultraviolet divergences and Moser's theorem
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1998
%P 545-593
%V 26
%N 3
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1998_4_26_3_545_0/
%G en
%F ASNSP_1998_4_26_3_545_0
Bonetto, Federico; Gallavotti, Giovanni; Gentile, Guido; Mastropietro, Vieri. Lindstedt series, ultraviolet divergences and Moser's theorem. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 3, pp. 545-593. http://www.numdam.org/item/ASNSP_1998_4_26_3_545_0/

[BG] G. Benfatto - G. Gallavotti, "Renormalization Group", Princeton University Press, Princeton, 1995. | MR | Zbl

[CF] L. Chierchia - C. Falcolini, A direct proof of a theorem by Kolmogorov in Hamiltonians systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (IV) 21 (1994), 541-593. | Numdam | MR | Zbl

[E] L.H. Eliasson, Absolutely convergent series expansions for quasi-periodic motions, Math. Phy. Electron. J. 2 (1996). | MR | Zbl

[G1] G. Gallavotti, Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods, Rev. Mod. Phys. 57 (1985), 471- 572. | MR

[G2] G. Gallavotti, Twistless KAM tori, Comm. Math. Phys. 164 (1994), 145-156. | MR | Zbl

[G3] G. Gallavotti, Invariant tori: a field theoretic point of view on Eliasson's work, In "Advances in Dynamical Systems and Quantum Physics", R. Figari (ed.), World Scientific, Singapore, 1995, pp. 117-132. | MR

[GGM] G. Gallavotti - G. Gentile - V. Mastropietro, Field theory and KAM tori, Math. Phy. Electron. J. 1 (1995). | MR | Zbl

[GG] G. Gallavotti - G. Gentile, Majorant series convergence for twistless KAM tori, Ergodic Theory Dynam. Systems 15 (1995), 857-869. | MR | Zbl

[GM1] G. Gentile - V. Mastropietro, KAM theorem revisited, Phys. D 90 (1996), 225-234. | MR | Zbl

[GM2] G. Gentile - V. Mastropietro, Tree expansion and multiscale analysis for KAM tori, Nonlinearity 8, (1995), 1159-1178. | MR | Zbl

[GM3] G. Gentile - V. Mastropietro, Methods for the analysis of the Lindstedt series for KAM tori and renormalizability in classical mechanics, A review with some applications, Rev. Math. Phys. 8 (1996), 393-444. | MR | Zbl

[H] M. Hermann, Difféomrphismes du cercles et rotations, Publ. Math. IHES 49 (1979), 1-233. | Numdam

[HP] F. Harary - E. Palmer, "Graphical enumeration", Academic Press, New York, 1973. | MR | Zbl

[K] A.N. Kolmogorov, On the preservation of conditionally periodic motions, Doklady Akademia Nauk SSSR 96 (1954), 527-530; english translation in G. Casati, J. Ford: Stochastic behavior in classical and quantum Hamiltonians, Lectures Notes in Physics 93, Springer, Berlin, 1979.

[M1] J. Moser, On invariant curves of an area preserving mapping of the annulus, Nac. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 1- 20, (1962). | MR | Zbl

[M2] J. Moser, A rapidly convergent iteration method and nonlinear differential equations II, Ann. Scuola Norm. Sup. Pisa Cl. Sci (III) 20 (1966),499-535. | Numdam | MR

[M3] J. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann. 169 (1967), 136-176. | MR | Zbl

[M4] J. Moser, On the construction of almost periodic solutions for ordinary differential equations, In "Proceedings of the International Conference of Functional Analysis and Related Topics", Tokyo (1969), pp. 60-67. | MR | Zbl

[M5] J. Moser, "Stable and Random Motions in Dynamical Systems, with special emphasis on Celestial Mechanics", Annals of Mathematical Studies 77, Princeton University Press, Princeton, 1973. | MR | Zbl

[Pö] J. Pöschel, Invariant manifolds of complex analytic mappings, In "Critical Phenomena, Random Systems, Gauge Theories", Les Houches, Session XLIII (1984), Vol. II, K. Osterwalder R. Stora (eds.), North Holland, 1986, pp. 949-964. | MR | Zbl

[PV] I. Percival - F. Vivaldi, Critical dynamics and diagrams, Phys. 33 (1988), 304-313. | MR | Zbl

[S] K. Siegel, Iterations of analytic functions, Ann. of Math. 43 (1942), 607- 612. | MR | Zbl

[SW] E. Stein - G. Weiss, "Introduction to Fourier analysis on Euclidean spaces", Princeton University Press, Princeton, 1971. | MR | Zbl