An exponential estimate of the time of stability of nearly-integrable hamiltonian systems

Russian Mathematical Surveys

Volumn 32, Issue 6, 1977, Pages 1-65

  Nekhoroshev, N N ^a  

^a NONE   (United States)

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EID: 84908024292     PISSN: 00360279     EISSN: None     Source Type: Journal    
DOI: 10.1070/RM1977v032n06ABEH003859     Document Type: Article

References (55)

1. Nekhoroshev N N 1971 Behaviour of nearly integrable Hamiltonian systems Funktsional. Anal i Prilozhen. 5 (4) 82-83.
2. Nekhoroshev N N 1971 Functional Anal. Appl. 5 338-339.
3. Poincaré H 1892-1893, 1899 Les méthodes nouvelles de le mécanique céleste 3 Vols (Paris).
4. Poincaré H 1971-1974 Izbrannye trudy (Nauka, Moscow) Translation.
5. Birkhoff G 1927 Dynamical systems (Amer. Math. Soc. Coll. Publ. 9) (Amer. Math. Soc, New York).
6. Birkhoff G 1941 Dinamicheskie sistemy (Gostekhizdat, Moscow-Leningrad) Translation.
7. Siegel C L 1952 Über die Existenz einer Normal form analytischer Hamiltonscher differentialgleichungen in der Nähe einer Gleichgewichtclösung Math. Ann. 128 144-170.
8. Siegel C L 1961 Über die Existenz einer Normal form analytischer Hamiltonscher differentialgleichungen in der Nähe einer Gleichgewichtclösung Mathematika 5 (2) 129-156.
9. Siegel C L 1956 Vorllesungen über Himelsmechanik (Springer-Verlag, Berlin-Göttingen-Heidelberg).
10. Siegel C L 1959 Lektsiipo nebesnoi mekhanike (Izdat. Inostr. Lit., Moscow) Translation.
11. Kolmogorov A N 1954 On the conservation of conditionally periodic motions for a small change in the Hamiltonian Dokl. Akad. Nauk SSSR 98 527-530.
12. Kolmogorov A N 1961 The general theory of dynamical systems and classical mechanics Mezhdunarodnyi Matematicheskii Kongress v Amsterdame, (Internat. Congress Mathematicians, Amsterdam) (Fizmatgiz, Moscow) p 187-208.
13. Arnol'd V I 1963 Proof of a theorem of A. N. Kolmogorov on the invariance of conditionally periodic motions under small perturbations of the Hamiltonian Uspekhi Mat. Nauk 18 (5) 13-40.
14. Arnol'd V I 1963 Russian Math. Surveys 18 (5) 9-36.
15. Arnol'd V I 1963 Small denominators and problems of stability of motion in classical and celestial mechanics Uspekhi Mat. Nauk 18 (6) 91-192.
16. Arnol'd V I 1963 Russian Math. Surveys 18 (6) 85-191.
17. Arnold V I and A Avez 1968 Ergodic problems of classical mechanics (Benjamin, New York-Amsterdam).
18. Arnol'd V I 1964 Instability of dynamical systems with many degrees of freedom Dokl. Akad. Nauk SSSR 156 9-12.
19. Arnol'd V I 1964 Soviet Math. Dokl. 5 581-585.
20. Moser J K 1962 On invariant curves of area-preserving mappings of an annulus (Nachr. Akad. Wiss. Gottingen, Math.-Phys. Kl. II) p 1-20.
21. Moser J K 1962 Matematika 6 (5) 51-67.
22. Moser J K 1961 A rapidly convergent iteration method and non-linear partial differential equations, I, II Ann. Scuola Norm. Sup. Pisa (3) 20 265-315.
23. Moser J K 1968 Uspekhi Mat. Nauk 23 (4) 179-238.
24. Zaslavskii G M and B V Cherikov 1971 Stochastic instability of non-linear oscillations Uspekhi Fiz. Nauk 105 (1) 3-40.
25. Zaslavskii G M and B V Cherikov 1971-1972 Soviet Phys. Uspekhi 14 549-568.
26. Arnol'd V I 1968 A stability problem and ergodic properties of classical dynamical systems Proc. Internat. Congress Mathematicians (Moscow 1966) ("Mir", Moscow) p 387-392.
27. Arnol'd V I 1968 Am. Math. Soc. Transl. (2) 70 5-11.
28. Glimm J 1964 Formal stability of Hamiltonian systems Comm. Pure Appl. Math. 17 509-526.
29. Nekhoroshev N N 1973 Stable lower estimates for smooth mappings and for gradients of smooth functions Mat. Sb. 90 432-478.
30. Nekhoroshev N N 1973 Math. USSR-Sb. 19 425-467.
31. Moser J K 1960 On the elimination of the irrationality condition and Birkhoff's concept of complete stability Bol. Soc. Mat. Mexicana (2) 5 167-175.
32. Khapaev M M 1970 Generalization of Lyapunov's second method and the investigation of some resonance problems Dokl. Akad. Nauk SSSR 193 46-49.
33. Khapaev M M 1970 Soviet Math. Dokl. 11 868-872.
34. Beletskii V V 1975 Dvizhenie sputnika otnositel'no tsentra mass v gravitatsionnom pole (Motion of a satellite relative to its centre of mass in a gravitational field) (Izv. Moskov. Gos. Univ., Moscow).
35. Moser J K 1968 Lectures on Hamiltonian systems (Mem. Amer. Math. Soc. 81) (Amer. Math. Soc, Providence, R.I.).
36. Moser J K 1973 Lektsiio gamil'tonovykh sistemakh (Mir, Moscow) Translation.
37. Moser J K 1955 Stabilitätsverhalten kanonischer Differentialgleichungssysteme (Nachr. Akad. Wiss. Gottingen, Math.-Phys. Kl. Ha) p 87-120.
38. Moser J K 1958 New aspects in the theory of stability of Hamiltonian systems Comm. Pure Appl. Math. 11 81-114.
39. Contopoulos G 1963 On the existence of a third integral of motion Astron. J. 68 1-14.
40. Hénon M and C Heiles 1964 The applicability of the third integral of motion; some numerical experiments Astron. J. 69 73-79.
41. Bryuno A D 1967 Formal stability of Hamiltonian systems Mat. Zametki 1 325-330.
42. Bryuno A D 1967 Math. Notes 1 216-219.
43. Arnol'd V I 1974 Matematicheskie motody klassicheskoi mekhaniki (Mathematical methods of classical mechanics) (Nauka, Moscow).
44. Bourbaki N 1942-1947 Eléments de mathématique. Partie I. Les structures fondamentales de l'analyse. Livre III Topologie générale Chaps. III-VIII (Actualities Sci. Ind. No. 916 and No. 1029) (Hermann, Paris).
45. Bourbaki N 1969 Obshchaya topologiya. Chisla isvyazannye s nimi gruppy i pros trans tva (Nauka, Moscow) Translation.
46. Cherikov B V 1969 Investigation of the theory of a non-linear resonance and the stochastic property Dissertation Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk.
47. Arnol'd V I 1961 Small denominators, I, Mapping the circle onto itself Izv. Akad. Nauk SSSR Ser. Mat. 25 21-86.
48. Rüssman H 1970 Über invariante Kurven differenzierbarer Abbildungen eines Kreisringes (Kleine Nenner. I) Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. IIa 67-105.
49. Rüssman H 1972 Kleine Nenner II. Bermerkungen zur Newtonschen Methode (Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II) p 1-10.
50. Zehnder E 1975 Generalized implicit function theorems with applications to some small divisor problems. I Comm. Pure Appl. Math. 28 91-140.
51. Zehnder E 1976 Generalized implicit function theorems with applications to some small divisor problems. II Comm. Pure Appl. Math. 29 49-111.
52. Neishtadt A I 1975 Passage through a resonance in a two frequency problem Dokl. Akad. Nauk SSSR 221 301-304.
53. Neishtadt A I 1975 Soviet Phys. Dokl. 20 189-191.
54. Neishtadt A I 1976 Certain resonance problems in non-linear systems Dissertation (Moscow State Univ., Moscow).
55. Arnol'd V I 1974 Nekotorye zadachi teorii differentsial'nykh uravnenii. Tezisy lektsii (Lectures notes: Some problems in the theory of differential equations) (Moscow).