Abstract
A selfcontained proof of the KAM theorem in the Thirring model is discussed.
Similar content being viewed by others
References
[A] Arnold, V.: Proof of a A. N. Kolmogorov theorem on conservation of conditionally periodic motions under small perturbations of the hamiltonian function. Uspeki Mat. Nauk18, 13–40 (1963)
[BG] Benfatto, G., Gallavotti, G.: Perturbation theory of the Fermi surface in a quantum liquid. A general quasi particle formalism and one dimensional systems. J. Stat. Phys.59, 541–664 (1990)
[BG1] Benfatto, G., Gallavotti, G.: Renormalization group application to the theory of the Fermi surface. Phys. Rev. B42, 9967–9972 (1990)
[B] Brjuno, A.: The analytic form of differential equations. I. Transactions of the Moscow Mathematical Society,25, 131–288 (1971); and II:26, 199–239 (1972)
[Br] Brydges, D.: Functional integrals and their applications. Notes with the collaboration of R. Fernandez; (Notes for a course for the Troisieme Cycle de la Physique en Suisse Romande given in Lausanne, Switzerland, 1992, archived in mp_arc@math.utexas.edu,#93-24, 1993
[E] Eliasson, L.H.: Hamiltonian systems with linear normal form near an invariant torus. Turchetti, G. (ed.) Bologna Conference, 30/5 to 3/6 1988, Singapore: World Scientific, 1989. And Generalization of an estimate of small divisors by Siegel, ed. E. Zehnder, P. Rabinowitz, book in honor of J. Moser, New York, London: Academic Press, 1990. But mainly: Absolutely convergent series expansions for quasi-periodic motions. Report 2-88, Dept. of Math., University of Stockholm, 1988
[G] Gallavotti, G.: Twistless KAM tori, quasi flat homoclinic intersection, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review. Deposited in the archive mp_arc@math.utexas.edu, #93-164
[G2] Gallavotti, G.: The elements of mechanics. Berlin, Heidelberg, New York: Springer 1983
[G3] Gallavotti, G.: Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods. Rev. Mod. Phys.57, 471–572 (1985). See also, Gallavotti, G.: Quasi integrable mechanical systems. Les Houches, XLIII (1984), vol. II, pp. 539–624, Osterwalder, K., Stora, R. (eds.) Amsterdam: North Holland, 1986
[G4] Gallavotti, G.: Perturbation theory. Notes in margin to the Mathematical Physics towards the XXI century conference, University of Negev, Beer Sheva, 14–19 March, 1993. This text will be archived in the archive mp_arc@math.utexas.edu, and it will appear in the Conference Proceedings
[G5] Gallavotti, G., Gentile, G.: Non-recursive proof of the KAM theorem. Preprint, p. 1–8. Agosto, 1993, Roma, archived in mp_arc@math.utexas.edu,#93-229
[K] Kolmogorov, N.: On the preservation of conditionally periodic motions. Dokl. Akad. Nauk SSSR96, 527–530 (1954). See also: Benettin, G., Galgani, L., Giorgilli, A., Strelcyn, J.M.: A proof of Kolmogorov theorem on invariant tori using canonical transformations defined by the Lie method. Nuovo Cimento79B, 201–223 (1984)
[M] Moser, J.: On invariant curves of an area preserving mapping of the annulus. Nachrichten Akademie Wiss. Göttingen11, 1–20 (1962)
[P] Pöschel, J.: Invariant manifolds of complex analytic mappings. Les Houches, XLIII (1984), Vol. II, p. 949–964, Osterwalder, K., Stora, R. (eds.) Amsterdam: North-Holland, 1986
[PV] Percival, I., Vivaldi, F.: Critical dynamics and diagrams. Physica D33, 304–313 (1988)
[S] Siegel, K.: Iterations of analytic functions. Ann. Math.43, 607–612 (1943)
[T] Thirring, W.: Course in mathematical physics Vol. 1, p. 133, Wien: Springer 1983
[V] Vittot, M.: Lindstedt perturbation series in hamiltonian mechanics: Explicit formulation via a multidimensional Burmann-Lagrange formula. Preprint CNRS-Luminy, case 907, F-13288, Marseille, 1992
Author information
Authors and Affiliations
Additional information
Communicated by J.-P. Eckmann
Archived in mp_arc@math.utexas.edu#93-172;to get a TeX version, send an empty E-mail message
Rights and permissions
About this article
Cite this article
Gallavotti, G. Twistless KAM tori. Commun.Math. Phys. 164, 145–156 (1994). https://doi.org/10.1007/BF02108809
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02108809