@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://archive.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://archive.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://archive.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://archive.numdam.org/item/ASNSP_1994_4_21_4_541_0/
[1] 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] 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] On the complex analytic structure of the golden-mean invariant curve for the standard map. Nonlinearity 3 (1990), 39-44. | MR | Zbl
- ,[4] Natural boundaries for area-preserving twist maps. J. Statist. Phys., 66 (1992), 1613-1630. | MR | Zbl
- - - ,[5] Graph Theory. Springer-Verlag (Graduate text in mathematics, 63), Berlin-Heidelberg-New York, 1979. | MR | Zbl
,[6] 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] Construction of analytic KAM surfaces and effective stability bounds, Comm. Math. Phys. 118 (1988), 119-161. | MR | Zbl
- ,[8] Drift and Diffusion in phase space, Preprint (1992). To appear in Ann. Inst. H. Poincaré Phys. Théor. | Numdam | MR | Zbl
- ,[9] Second order Hamiltonian equations on T∞ and almost-periodic solutions. Preprint (1992). To appear in J. Differential Equations. | Zbl
- ,[10] Asymptotic expansions of quasiperiodic solutions. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. (4), 16 (1989), 245-258. | Numdam | MR | Zbl
- ,[11] Absolutely convergent series expansions for quasi periodic motions, Reports Department of Math., Univ. of Stockholm, Sweden, No. 2 (1988), 1-31. | MR
,[12] Hamiltonian systems with linear normal form near an invariant torus. In "Nonlinear Dynamics", G. Turchetti (Ed.) World Scientific, Singapore, 1989. | MR
,[13] 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] Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors, J. Statist. Phys. 67 (1992). | MR | Zbl
- ,[15] 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] Non recursive proof of the KAM theorem. Preprint (1993).
- ,[17] Combinatorial Enumeration. Wyley Interscience Series in Discrete Math., 1983. | MR | Zbl
- ,[18] Graph Theory. Addison-Wesley, 1969. | MR | Zbl
,[19] 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] 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] Convergent series expansions for quasi-periodic motions. Math. Ann. 169 (1967), 136-176. | MR | Zbl
,[22] 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] Les méthodes nouvelles de la mécanique céleste. Vols. 1-3. Gauthier-Villars, Paris 1892/1893/1899.
,[24] 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] Diophantine Approximation, Springer-Verlag (Lecture Notes in Math. 785), Berlin-Heidelberg -New York, 1980. | MR | Zbl
,[26] Iterations of analytic functions, Ann. of Math. 43 (1942), 607-612. | MR | Zbl
,[27] Lindstedt perturbation series in Hamiltonian mechanics: explicit formulation via a multidimensional Burmann-Lagrange formula, Preprint (1991).
,