A direct proof of a theorem by Kolmogorov in hamiltonian systems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 21 (1994) no. 4, pp. 541-593. 
@article{ASNSP_1994_4_21_4_541_0,
     author = {Chierchia, L. and Falcolini, C.},
     title = {A direct proof of a theorem by {Kolmogorov} in hamiltonian systems},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {541--593},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 21},
     number = {4},
     year = {1994},
     zbl = {0836.34040},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1994_4_21_4_541_0/}
}
TY  - JOUR
AU  - Chierchia, L.
AU  - Falcolini, C.
TI  - A direct proof of a theorem by Kolmogorov in hamiltonian systems
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1994
SP  - 541
EP  - 593
VL  - 21
IS  - 4
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1994_4_21_4_541_0/
LA  - en
ID  - ASNSP_1994_4_21_4_541_0
ER  - 
%0 Journal Article
%A Chierchia, L.
%A Falcolini, C.
%T A direct proof of a theorem by Kolmogorov in hamiltonian systems
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1994
%P 541-593
%V 21
%N 4
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1994_4_21_4_541_0/
%G en
%F ASNSP_1994_4_21_4_541_0
Chierchia, L.; Falcolini, C. A direct proof of a theorem by Kolmogorov in hamiltonian systems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 21 (1994) no. 4, pp. 541-593. http://www.numdam.org/item/ASNSP_1994_4_21_4_541_0/

[1] V.I. Arnold, Proof of A.N. Kolmogorov's theorem on the preservation of quasiperiodic motions under small perturbation of the Hamiltonian. Uspekhi Mat. Nauk 18, No. 5 (1963), 13-40 (Russian); English translation: Russian Math. Surveys 18, No. 5 (1963), 9-36. | MR | Zbl

[2] V.I. Arnold, Small denominators and problems of stability of motions in classical and celestial mechanics. Uspekhi Mat. Nauk 18, No. 6 (1963), 91-192 (Russian); English translation: Russian Math. Surveys 18, No. 6 (1963), 85-192. | MR | Zbl

[3] A. Berretti - L. Chierchia, On the complex analytic structure of the golden-mean invariant curve for the standard map. Nonlinearity 3 (1990), 39-44. | MR | Zbl

[4] A. Berretti - A. Celletti - L. Chierchia - C. Falcolini, Natural boundaries for area-preserving twist maps. J. Statist. Phys., 66 (1992), 1613-1630. | MR | Zbl

[5] B. Bollobas, Graph Theory. Springer-Verlag (Graduate text in mathematics, 63), Berlin-Heidelberg-New York, 1979. | MR | Zbl

[6] A.D. Brjuno, Convergence of transformations of differential equations to normal form. Dokl. Akad. Nauk SSSR 165 (1965), 987-989; Analytic form of differential equations, Trans. Moscow Math. Soc. 25 (1971), 131-288 and 26 (1972), 199-239. | MR | Zbl

[7] A. Celetti - L. Chierchia, Construction of analytic KAM surfaces and effective stability bounds, Comm. Math. Phys. 118 (1988), 119-161. | MR | Zbl

[8] L. Chierchia - G. Gallavotti, Drift and Diffusion in phase space, Preprint (1992). To appear in Ann. Inst. H. Poincaré Phys. Théor. | Numdam | MR | Zbl

[9] L. Chierchia - P. Perfetti, Second order Hamiltonian equations on T∞ and almost-periodic solutions. Preprint (1992). To appear in J. Differential Equations. | Zbl

[10] L. Chierchia - E. Zehnder, Asymptotic expansions of quasiperiodic solutions. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4), 16 (1989), 245-258. | Numdam | MR | Zbl

[11] L.H. Eliasson, Absolutely convergent series expansions for quasi periodic motions, Reports Department of Math., Univ. of Stockholm, Sweden, No. 2 (1988), 1-31. | MR

[12] L.H. Eliasson, Hamiltonian systems with linear normal form near an invariant torus. In "Nonlinear Dynamics", G. Turchetti (Ed.) World Scientific, Singapore, 1989. | MR

[13] L.H. Eliasson, Generalization of an estimate of small divisors by Siegel. In "Analysis, et cetera", P.H. Rabinowitz and E. Zehnder (Eds.), Academic Press, 1990. | MR | Zbl

[14] C. Falcolini - R. De La Llave, Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors, J. Statist. Phys. 67 (1992). | MR | Zbl

[15] G. Gallavotti, Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review. Preprint (1993). | MR | Zbl

[16] G. Gallavotti - G. Gentile, Non recursive proof of the KAM theorem. Preprint (1993).

[17] I.P. Goulden - D.M. Jackson, Combinatorial Enumeration. Wyley Interscience Series in Discrete Math., 1983. | MR | Zbl

[18] F. Harary, Graph Theory. Addison-Wesley, 1969. | MR | Zbl

[19] A.N. Kolmogorov, On conservation of conditionally periodic motions under small perturbations of the Hamiltonian. Dokl. Akad. Nauk SSSR 98, No. 4 (1954), 527-530 (Russian). | MR | Zbl

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

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

[22] J. Moser, A rapidly convergent iteration method and nonlinear partial differential equations, I-II. Ann. Scuola Norm. Super. Pisa Cl. Sci. (3) 20 (1966), 265-315 and 499-535. | Numdam | Zbl

[23] H. Poincaré, Les méthodes nouvelles de la mécanique céleste. Vols. 1-3. Gauthier-Villars, Paris 1892/1893/1899.

[24] H. Rüssmann, Kleine Nenner. I: Über invariante Kurven differenzierbarer Abbildungen eines Kreisringes. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 1970 (1970), 67-105. | MR | Zbl

[25] W.M. Schmidt, Diophantine Approximation, Springer-Verlag (Lecture Notes in Math. 785), Berlin-Heidelberg -New York, 1980. | MR | Zbl

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

[27] M. Vittot, Lindstedt perturbation series in Hamiltonian mechanics: explicit formulation via a multidimensional Burmann-Lagrange formula, Preprint (1991).