Lindstedt series, ultraviolet divergences and Moser's theorem
Federico Bonetto; Giovanni Gallavotti; Guido Gentile; Vieri Mastropietro
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)
- Volume: 26, Issue: 3, page 545-593
- ISSN: 0391-173X
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topBonetto, Federico, et al. "Lindstedt series, ultraviolet divergences and Moser's theorem." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.3 (1998): 545-593. <http://eudml.org/doc/84338>.
@article{Bonetto1998,
author = {Bonetto, Federico, Gallavotti, Giovanni, Gentile, Guido, Mastropietro, Vieri},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Lindstedt series; Thirring model; invariant tori; quasi integrable even Hamiltonian; Lindstedt algorithm; Kolmogorov's invariant tori; non renormalizable quantum field theory},
language = {eng},
number = {3},
pages = {545-593},
publisher = {Scuola normale superiore},
title = {Lindstedt series, ultraviolet divergences and Moser's theorem},
url = {http://eudml.org/doc/84338},
volume = {26},
year = {1998},
}
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
PB - Scuola normale superiore
VL - 26
IS - 3
SP - 545
EP - 593
LA - eng
KW - Lindstedt series; Thirring model; invariant tori; quasi integrable even Hamiltonian; Lindstedt algorithm; Kolmogorov's invariant tori; non renormalizable quantum field theory
UR - http://eudml.org/doc/84338
ER -
References
top- [BG] G. Benfatto - G. Gallavotti, "Renormalization Group", Princeton University Press, Princeton, 1995. Zbl0830.58038MR1380265
- [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. Zbl0836.34040MR1318772
- [E] L.H. Eliasson, Absolutely convergent series expansions for quasi-periodic motions, Math. Phy. Electron. J.2 (1996). Zbl0896.34035MR1399458
- [G1] G. Gallavotti, Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods, Rev. Mod. Phys.57 (1985), 471- 572. MR789582
- [G2] G. Gallavotti, Twistless KAM tori, Comm. Math. Phys.164 (1994), 145-156. Zbl0805.58054MR1288156
- [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. MR1414693
- [GGM] G. Gallavotti - G. Gentile - V. Mastropietro, Field theory and KAM tori, Math. Phy. Electron. J. 1 (1995). Zbl0849.58038MR1359460
- [GG] G. Gallavotti - G. Gentile, Majorant series convergence for twistless KAM tori, Ergodic Theory Dynam. Systems15 (1995), 857-869. Zbl0871.58040MR1356618
- [GM1] G. Gentile - V. Mastropietro, KAM theorem revisited, Phys.D90 (1996), 225-234. Zbl0896.58030MR1372451
- [GM2] G. Gentile - V. Mastropietro, Tree expansion and multiscale analysis for KAM tori, Nonlinearity8, (1995), 1159-1178. Zbl0841.58037MR1363405
- [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. Zbl0870.70012MR1388257
- [H] M. Hermann, Difféomrphismes du cercles et rotations, Publ. Math. IHES49 (1979), 1-233.
- [HP] F. Harary - E. Palmer, "Graphical enumeration", Academic Press, New York, 1973. Zbl0266.05108MR357214
- [K] A.N. Kolmogorov, On the preservation of conditionally periodic motions, Doklady Akademia Nauk SSSR96 (1954), 527-530; english translation in G. Casati, J. Ford: Stochastic behavior in classical and quantum Hamiltonians, Lectures Notes in Physics93, Springer, Berlin, 1979. Zbl0056.31502
- [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). Zbl0107.29301MR147741
- [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. MR206461
- [M3] J. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann.169 (1967), 136-176. Zbl0149.29903MR208078
- [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. Zbl0201.41701MR265692
- [M5] J. Moser, "Stable and Random Motions in Dynamical Systems, with special emphasis on Celestial Mechanics", Annals of Mathematical Studies77, Princeton University Press, Princeton, 1973. Zbl0271.70009MR442980
- [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. Zbl0681.58037MR880541
- [PV] I. Percival - F. Vivaldi, Critical dynamics and diagrams, Phys.33 (1988), 304-313. Zbl0662.58038MR984624
- [S] K. Siegel, Iterations of analytic functions, Ann. of Math.43 (1942), 607- 612. Zbl0061.14904MR7044
- [SW] E. Stein - G. Weiss, "Introduction to Fourier analysis on Euclidean spaces", Princeton University Press, Princeton, 1971. Zbl0232.42007MR304972
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