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Volumn 41, Issue 4, 2004, Pages 507-521

Kam theory: The legacy of kolmogorov's 1954 paper

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EID: 13844316334     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-04-01009-2     Document Type: Article
Times cited : (46)

References (82)
  • 1
    • 0002764805 scopus 로고
    • Proof of a theorem by A.N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian
    • V.I. Arnold, Proof of a theorem by A.N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian, Usp. Math. Nauk 18(5) (1963) 13-40; Russ. Math. Surv. 18(5) (1963) 9-36. MR 29:328
    • (1963) Usp. Math. Nauk , vol.18 , Issue.5 , pp. 13-40
    • Arnold, V.I.1
  • 2
    • 0348094266 scopus 로고
    • MR 29:328
    • V.I. Arnold, Proof of a theorem by A.N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian, Usp. Math. Nauk 18(5) (1963) 13-40; Russ. Math. Surv. 18(5) (1963) 9-36. MR 29:328
    • (1963) Russ. Math. Surv. , vol.18 , Issue.5 , pp. 9-36
  • 3
    • 0002356196 scopus 로고
    • Small denominators and problems of stability of motion in classical and celestial mechanics
    • V.I. Arnold, Small denominators and problems of stability of motion in classical and celestial mechanics, Russian Math. Surveys 18(6) (1963) 85-191. [Corrigenda (in Russian): Uspekhi Mat. Nauk 23 (1968) 216.] MR 30:943
    • (1963) Russian Math. Surveys , vol.18 , Issue.6 , pp. 85-191
    • Arnold, V.I.1
  • 4
    • 70350723163 scopus 로고
    • Corrigenda (in Russian): MR 30:943
    • V.I. Arnold, Small denominators and problems of stability of motion in classical and celestial mechanics, Russian Math. Surveys 18(6) (1963) 85-191. [Corrigenda (in Russian): Uspekhi Mat. Nauk 23 (1968) 216.] MR 30:943
    • (1968) Uspekhi Mat. Nauk , vol.23 , pp. 216
  • 5
    • 0000877933 scopus 로고
    • Instability of dynamical systems with many degrees of freedom
    • MR 29:329
    • V.I. Arnold, Instability of dynamical systems with many degrees of freedom, Soviet Mathematics 5(3) (1964) 581-585. MR 29:329
    • (1964) Soviet Mathematics , vol.5 , Issue.3 , pp. 581-585
    • Arnold, V.I.1
  • 6
    • 0000071902 scopus 로고
    • Small divisors I: On mappings of the circle onto itself
    • V.I. Arnold, Small divisors I: On mappings of the circle onto itself, Amer. Math. Soc. Transl., Ser.2 46 (1965) 213-284. [Russian original: Izvest. Akad. Nauk SSSR, Ser Mat. 25(1) (1961) 21-86; Corrigenda: ibid. 28(2) (1964) 479-480.] MR 25:4113
    • (1965) Amer. Math. Soc. Transl., Ser.2 , vol.46 , pp. 213-284
    • Arnold, V.I.1
  • 7
    • 13844322094 scopus 로고
    • Russian original
    • V.I. Arnold, Small divisors I: On mappings of the circle onto itself, Amer. Math. Soc. Transl., Ser.2 46 (1965) 213-284. [Russian original: Izvest. Akad. Nauk SSSR, Ser Mat. 25(1) (1961) 21-86; Corrigenda: ibid. 28(2) (1964) 479-480.] MR 25:4113
    • (1961) Izvest. Akad. Nauk SSSR, Ser Mat. , vol.25 , Issue.1 , pp. 21-86
  • 8
    • 13844322093 scopus 로고
    • Corrigenda: MR 25:4113
    • V.I. Arnold, Small divisors I: On mappings of the circle onto itself, Amer. Math. Soc. Transl., Ser.2 46 (1965) 213-284. [Russian original: Izvest. Akad. Nauk SSSR, Ser Mat. 25(1) (1961) 21-86; Corrigenda: ibid. 28(2) (1964) 479-480.] MR 25:4113
    • (1964) Izvest. Akad. Nauk SSSR, Ser Mat. , vol.28 , Issue.2 , pp. 479-480
  • 10
    • 0003978095 scopus 로고
    • Springer Verlag 2nd edition [Russian original: Nauka 1974.] MR 57:14033b, MR 90c:58046
    • V.I. Arnold, Mathematical Methods in Classical Mechanics. Springer Verlag 1978, 2nd edition 1989. [Russian original: Nauka 1974.] MR 57:14033b, MR 90c:58046
    • (1978) Mathematical Methods in Classical Mechanics
    • Arnold, V.I.1
  • 12
    • 0347125069 scopus 로고    scopus 로고
    • Science of Chaos or Chaos in Science?
    • P.R. Gross, N. Levitt and M.W. Lewis (eds.), Ann. of the New York Academy of Sciences New York Academy of Sciences, New York
    • J. Bricmont, Science of Chaos or Chaos in Science? In P.R. Gross, N. Levitt and M.W. Lewis (eds.), The Flight from Science and Reason, Ann. of the New York Academy of Sciences 775 131-175, New York Academy of Sciences, New York 1996. [Also appeared in Physicalia Magazine 17 (1995) 159-208.] MR 99h:00012
    • (1996) The Flight from Science and Reason , vol.775 , pp. 131-175
    • Bricmont, J.1
  • 13
    • 0347125069 scopus 로고    scopus 로고
    • MR 99h:00012
    • J. Bricmont, Science of Chaos or Chaos in Science? In P.R. Gross, N. Levitt and M.W. Lewis (eds.), The Flight from Science and Reason, Ann. of the New York Academy of Sciences 775 131-175, New York Academy of Sciences, New York 1996. [Also appeared in Physicalia Magazine 17 (1995) 159-208.] MR 99h:00012
    • (1995) Physicalia Magazine , vol.17 , pp. 159-208
  • 14
    • 0033243770 scopus 로고    scopus 로고
    • KAM theorem and quantum field theory
    • MR 2000d:37070
    • J. Bricmont, K. Gawedzki and A. Kupiainen, KAM Theorem and Quantum Field Theory, Comm. Math. Phys. 201 (1999) 699-727. MR 2000d:37070
    • (1999) Comm. Math. Phys. , vol.201 , pp. 699-727
    • Bricmont, J.1    Gawedzki, K.2    Kupiainen, A.3
  • 15
    • 84968494997 scopus 로고
    • Complex analytic dynamics on the Riemann sphere
    • MR 85h:58001
    • P. Blanchard, Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. (N.S.) 11(1) (1984) 85-141. MR 85h:58001
    • (1984) Bull. Amer. Math. Soc. (N.S.) , vol.11 , Issue.1 , pp. 85-141
    • Blanchard, P.1
  • 17
    • 0142137606 scopus 로고    scopus 로고
    • Normal-internal resonances in quasiperiodically forced oscillators: A conservative approach
    • H.W. Broer, H. Hanßmann, À. Jorba, J. Villanueva and F.O.O. Wagener, Normal-internal resonances in quasiperiodically forced oscillators: a conservative approach, Nonlinearity 16 (2003) 1751-1791.
    • (2003) Nonlinearity , vol.16 , pp. 1751-1791
    • Broer, H.W.1    Hanßmann, À.H.2    Villanueva, J.J.3    Wagener, F.O.O.4
  • 20
    • 0002321444 scopus 로고
    • A proof of the iso-energetic KAM-theorem from the 'ordinary' one
    • MR 92a:58117
    • H.W. Broer and G.B. Huitema, A proof of the iso-energetic KAM-theorem from the 'ordinary' one, Journ. Diff. Eqns. 90(1) (1991) 52-60. MR 92a:58117
    • (1991) Journ. Diff. Eqns. , vol.90 , Issue.1 , pp. 52-60
    • Broer, H.W.1    Huitema, G.B.2
  • 21
    • 0001302604 scopus 로고
    • Unfoldings of quasi-periodic tori in reversible systems
    • MR 96b:58099
    • H.W. Broer and G.B. Huitema, Unfoldings of quasi-periodic tori in reversible systems, Journ. Dynamics and Differential Equations 7(1) (1995) 191-212. MR 96b:58099
    • (1995) Journ. Dynamics and Differential Equations , vol.7 , Issue.1 , pp. 191-212
    • Broer, H.W.1    Huitema, G.B.2
  • 22
    • 0003210171 scopus 로고    scopus 로고
    • Quasi-periodic motions in families of dynamical systems: Order amidst chaos
    • Springer Verlag MR 99d:58142
    • H.W. Broer, G.B. Huitema and M.B. Sevryuk, Quasi-periodic motions in families of dynamical systems: order amidst chaos, LNM 1645. Springer Verlag 1996. MR 99d:58142
    • (1996) LNM , vol.1645
    • Broer, H.W.1    Huitema, G.B.2    Sevryuk, M.B.3
  • 23
    • 0041022502 scopus 로고
    • Unfoldings and bifurcations of quasi-periodic tori
    • MR 91e:58156
    • H.W. Broer, G.B. Huitema, F. Takens and B.L.J. Braaksma, Unfoldings and bifurcations of quasi-periodic tori, Mem. AMS 83(421) (1990) 1-170. MR 91e:58156
    • (1990) Mem. AMS , vol.83 , Issue.421 , pp. 1-170
    • Broer, H.W.1    Huitema, G.B.2    Takens, F.3    Braaksma, B.L.J.4
  • 24
    • 0242275980 scopus 로고    scopus 로고
    • Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation
    • H.W. Broer, J. Puig and C. Simó, Resonance tongues and instability pockets in the quasi-periodic Hill-Schrödinger equation, Commun. Math. Phys. 641 (2003) 467-503.
    • (2003) Commun. Math. Phys. , vol.641 , pp. 467-503
    • Broer, H.W.1    Puig, J.2    Simó, C.3
  • 25
    • 0004945477 scopus 로고
    • Convergence of transformations of differential equations to the normal forms
    • MR 33:325
    • A.D. Bruno, Convergence of transformations of differential equations to the normal forms, Dokl. Akad. Nauk. SSSR. 165 (1965) 987-989. MR 33:325
    • (1965) Dokl. Akad. Nauk. SSSR. , vol.165 , pp. 987-989
    • Bruno, A.D.1
  • 28
    • 84890642792 scopus 로고    scopus 로고
    • Survey on dissipative KAM theory including quasi-periodic bifurcations, based on lectures by Henk Broer
    • To appear in J. Montaldi and T. Ratiu (eds.): LMS Lecture Notes Series Cambridge University Press
    • M.C. Ciocci, A. Litvak-Hinenzon and H.W. Broer, Survey on dissipative KAM theory including quasi-periodic bifurcations, based on lectures by Henk Broer. To appear in J. Montaldi and T. Ratiu (eds.): Peyresq Lectures on Geometric Mechanics and Symmetry, LMS Lecture Notes Series 306. Cambridge University Press.
    • Peyresq Lectures on Geometric Mechanics and Symmetry , vol.306
    • Ciocci, M.C.1    Litvak-Hinenzon, A.2    Broer, H.W.3
  • 29
    • 0040279476 scopus 로고
    • Zum Zentrumproblem
    • H. Cremer, Zum Zentrumproblem, Math. Ann. 98 (1927) 151-163.
    • (1927) Math. Ann. , vol.98 , pp. 151-163
    • Cremer, H.1
  • 32
    • 34250407352 scopus 로고
    • The one-dimensional Schrödinger equation with a quasiperiodic potential
    • MR 57:10076
    • E.I. Dinaburg and Y.G. Sinai, The one-dimensional Schrödinger equation with a quasiperiodic potential. Func. Anal. and Appl. 9 (1975) 179-189. MR 57:10076
    • (1975) Func. Anal. and Appl. , vol.9 , pp. 179-189
    • Dinaburg, E.I.1    Sinai, Y.G.2
  • 34
    • 0000284780 scopus 로고
    • Absence of diffusion in the Anderson model for large disorder or low energy
    • MR 85c:82004
    • J. Fröhlich and T. Spencer, Absence of diffusion in the Anderson model for large disorder or low energy, Comm. Math. Phys. 88 (1983) 151-189. MR 85c:82004
    • (1983) Comm. Math. Phys. , vol.88 , pp. 151-189
    • Fröhlich, J.1    Spencer, T.2
  • 36
    • 13844314253 scopus 로고    scopus 로고
    • Aspects of the ergodic, qualitative and statistical theory of motion
    • To appear Springer Verlag
    • G. Gallavotti, F. Bonetto and G. Gentile, Aspects of the ergodic, qualitative and statistical theory of motion. To appear Springer Verlag. Preliminary version at http://ipparco.roma1.infn.it/libri.html.
    • Preliminary Version
    • Gallavotti, G.1    Bonetto, F.2    Gentile, G.3
  • 37
    • 0002810152 scopus 로고
    • Field theory and KAM tori
    • paper 5. MR 97b:81072
    • G. Gallavotti, G. Gentile and V. Mastropietro, Field theory and KAM tori, MPEJ 1 (1995) paper 5. MR 97b:81072
    • (1995) MPEJ , vol.1
    • Gallavotti, G.1    Gentile, G.2    Mastropietro, V.3
  • 38
    • 0010138127 scopus 로고    scopus 로고
    • The quasi-periodic centre-saddle bifurcation
    • MR 98m:58099
    • H. Hanßmann, The quasi-periodic centre-saddle bifurcation, Journ. Diff. Eqns. 142(2) (1998) 305-370. MR 98m:58099
    • (1998) Journ. Diff. Eqns. , vol.142 , Issue.2 , pp. 305-370
    • Hanßmann, H.1
  • 39
    • 51249187032 scopus 로고
    • Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations
    • MR 81h:58039
    • M.R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES 49 (1979) 5-234. MR 81h:58039
    • (1979) Publ. Math. IHES , vol.49 , pp. 5-234
    • Herman, M.R.1
  • 40
    • 84980080650 scopus 로고
    • A mathematical example displaying features of turbulence
    • MR 10:716a
    • E. Hopf, A mathematical example displaying features of turbulence. Commun. Appl. Math. 1 (1948) 303-322. MR 10:716a
    • (1948) Commun. Appl. Math. , vol.1 , pp. 303-322
    • Hopf, E.1
  • 42
    • 0040507795 scopus 로고    scopus 로고
    • On the normal behaviour of partially elliptic lower-dimensional tori of Hamiltonian systems
    • MR 98h:58169
    • A. Jorba and J. Villanueva, On the normal behaviour of partially elliptic lower-dimensional tori of Hamiltonian systems, Nonlinearity 10 (1997) 783-822. MR 98h:58169
    • (1997) Nonlinearity , vol.10 , pp. 783-822
    • Jorba, A.1    Villanueva, J.2
  • 44
    • 0001246972 scopus 로고
    • On the conservation of conditionally periodic motions for a small change in Hamilton's function
    • A.N. Kolmogorov, On the conservation of conditionally periodic motions for a small change in Hamilton's function [in Russian], Dokl. Akad. Nauk SSSR 98 (1954) 525-530; English translation in LNP 93 (1979) 51-56. MR 16:924c
    • (1954) Dokl. Akad. Nauk SSSR , vol.98 , pp. 525-530
    • Kolmogorov, A.N.1
  • 45
    • 0000152120 scopus 로고
    • English translation MR 16:924c
    • A.N. Kolmogorov, On the conservation of conditionally periodic motions for a small change in Hamilton's function [in Russian], Dokl. Akad. Nauk SSSR 98 (1954) 525-530; English translation in LNP 93 (1979) 51-56. MR 16:924c
    • (1979) LNP , vol.93 , pp. 51-56
  • 46
    • 0001441814 scopus 로고
    • The general theory of dynamical systems and classical mechanics
    • Amsterdam, North Holland, Amsterdam, 1957 [in Russian]
    • A.N. Kolmogorov, The general theory of dynamical systems and classical mechanics. Proceedings of the International Congress of Mathematicians (Amsterdam, 1954), Vol. 1, pages 315-333, North Holland, Amsterdam, 1957 [in Russian]. [Reprinted in: International Mathematical Congress in Amsterdam, 1954 (Plenary Lectures), pages 187-208. Fizmatgiz, Moscow 1961; English translation as Appendix D in R.H. Abraham, Foundations of Mechanics, pages 263-279. Benjamin, 1967. Reprinted as Appendix in R.H. Abraham and J.E. Marsden, Foundations of Mechanics, Second Edition, pages 741-757. Benjamin / Cummings 1978.] MR 20:4066
    • (1954) Proceedings of the International Congress of Mathematicians , vol.1 , pp. 315-333
    • Kolmogorov, A.N.1
  • 47
    • 84906694861 scopus 로고
    • Reprinted in: Fizmatgiz, Moscow
    • A.N. Kolmogorov, The general theory of dynamical systems and classical mechanics. Proceedings of the International Congress of Mathematicians (Amsterdam, 1954), Vol. 1, pages 315-333, North Holland, Amsterdam, 1957 [in Russian]. [Reprinted in: International Mathematical Congress in Amsterdam, 1954 (Plenary Lectures), pages 187-208. Fizmatgiz, Moscow 1961; English translation as Appendix D in R.H. Abraham, Foundations of Mechanics, pages 263-279. Benjamin, 1967. Reprinted as Appendix in R.H. Abraham and J.E. Marsden, Foundations of Mechanics, Second Edition, pages 741-757. Benjamin / Cummings 1978.] MR 20:4066
    • (1961) International Mathematical Congress in Amsterdam, 1954 (Plenary Lectures) , vol.1954 , pp. 187-208
  • 48
    • 0004282301 scopus 로고
    • English translation as Appendix D Benjamin
    • A.N. Kolmogorov, The general theory of dynamical systems and classical mechanics. Proceedings of the International Congress of Mathematicians (Amsterdam, 1954), Vol. 1, pages 315-333, North Holland, Amsterdam, 1957 [in Russian]. [Reprinted in: International Mathematical Congress in Amsterdam, 1954 (Plenary Lectures), pages 187-208. Fizmatgiz, Moscow 1961; English translation as Appendix D in R.H. Abraham, Foundations of Mechanics, pages 263-279. Benjamin, 1967. Reprinted as Appendix in R.H. Abraham and J.E. Marsden, Foundations of Mechanics, Second Edition, pages 741-757. Benjamin / Cummings 1978.] MR 20:4066
    • (1967) Foundations of Mechanics , pp. 263-279
    • Abraham, R.H.1
  • 49
    • 0004282301 scopus 로고
    • Reprinted as Appendix Benjamin / Cummings MR 20:4066
    • A.N. Kolmogorov, The general theory of dynamical systems and classical mechanics. Proceedings of the International Congress of Mathematicians (Amsterdam, 1954), Vol. 1, pages 315-333, North Holland, Amsterdam, 1957 [in Russian]. [Reprinted in: International Mathematical Congress in Amsterdam, 1954 (Plenary Lectures), pages 187-208. Fizmatgiz, Moscow 1961; English translation as Appendix D in R.H. Abraham, Foundations of Mechanics, pages 263-279. Benjamin, 1967. Reprinted as Appendix in R.H. Abraham and J.E. Marsden, Foundations of Mechanics, Second Edition, pages 741-757. Benjamin / Cummings 1978.] MR 20:4066
    • (1978) Foundations of Mechanics, Second Edition , pp. 741-757
    • Abraham, R.H.1    Marsden, J.E.2
  • 50
    • 0001836195 scopus 로고
    • Nearly integrable infinite-dimensional Hamiltonian systems
    • Springer Verlag MR 95k:58145
    • S.B. Kuksin, Nearly integrable infinite-dimensional Hamiltonian systems, LNM 1556 Springer Verlag 1993. MR 95k:58145
    • (1993) LNM , vol.1556
    • Kuksin, S.B.1
  • 52
    • 0002144874 scopus 로고
    • On the problem of turbulence
    • MR 6:246c
    • L.D. Landau, On the problem of turbulence, Akad. Nauk. 44 (1944) 311-314. MR 6:246c
    • (1944) Akad. Nauk. , vol.44 , pp. 311-314
    • Landau, L.D.1
  • 54
    • 13844311225 scopus 로고
    • Large scale chaos and marginal stability in the solar system
    • Int. Press Cambridge 1995. MR 96j:70015
    • J. Laskar, Large scale chaos and marginal stability in the solar system, Proceedings XIIth Int. Congress of Math. Phys. (Paris 1994), Int. Press Cambridge 1995. MR 96j:70015
    • (1994) Proceedings XIIth Int. Congress of Math. Phys. Paris
    • Laskar, J.1
  • 55
    • 0000882178 scopus 로고    scopus 로고
    • A tutorial on KAM Theory
    • A. Katok et al., eds., Proceedings of Symposia in Pure Mathematics MR 2002h:37123
    • R. de la Llave, A tutorial on KAM Theory. In A. Katok et al., eds., Proceedings of Symposia in Pure Mathematics 69, Amer. Math. Soc. (2001), 175-292. MR 2002h:37123
    • (2001) Amer. Math. Soc. , vol.69 , pp. 175-292
    • De La Llave, R.1
  • 56
    • 0040859457 scopus 로고
    • Proof of existence for breathers for time reversible or Hamiltonian networks of weakly coupled oscillators
    • MR 96a:34085
    • R.S. MacKay and S. Aubry, Proof of existence for breathers for time reversible or Hamiltonian networks of weakly coupled oscillators, Nonlinearity 7(6) (1994) 1623-1643. MR 96a:34085
    • (1994) Nonlinearity , vol.7 , Issue.6 , pp. 1623-1643
    • MacKay, R.S.1    Aubry, S.2
  • 58
    • 0001851184 scopus 로고
    • On invariant curves of area-preserving mappings of an annulus
    • MR 26:5255
    • J.K. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II. 1 (1962) 1-20. MR 26:5255
    • (1962) Nachr. Akad. Wiss. Göttingen, Math.-phys. Kl. II , vol.1 , pp. 1-20
    • Moser, J.K.1
  • 59
    • 0000446778 scopus 로고
    • On the theory of quasiperiodic motions
    • MR 34:3013
    • J.K. Moser, On the theory of quasiperiodic motions, SIAM Review 8(2) (1966) 145-172. MR 34:3013
    • (1966) SIAM Review , vol.8 , Issue.2 , pp. 145-172
    • Moser, J.K.1
  • 60
    • 3042570326 scopus 로고
    • Convergent series expansions for quasi-periodic motions
    • MR 34:7888
    • J.K. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann. 169 (1967) 136-176. MR 34:7888
    • (1967) Math. Ann. , vol.169 , pp. 136-176
    • Moser, J.K.1
  • 61
    • 0002945849 scopus 로고
    • Lectures on Hamiltonian systems
    • MR 37:6060
    • J.K. Moser, Lectures on Hamiltonian systems, Mem. AMS 81 (1968) 1-60. MR 37:6060
    • (1968) Mem. AMS , vol.81 , pp. 1-60
    • Moser, J.K.1
  • 62
    • 0003292012 scopus 로고
    • Stable and random motions in dynamical systems, with special emphasis to celestial mechanics
    • Princeton University Press MR 56:1355
    • J.K. Moser, Stable and random motions in dynamical systems, with special emphasis to celestial mechanics, Ann. Math. Studies 77. Princeton University Press 1973. MR 56:1355
    • (1973) Ann. Math. Studies , vol.77
    • Moser, J.K.1
  • 63
    • 84908024292 scopus 로고
    • Exponential estimate on the stability time of near integrable Hamiltonian systems
    • MR 58:18570
    • N.N. Nekhoroshev, Exponential estimate on the stability time of near integrable Hamiltonian systems, Russ. Math. Surveys 32(6) (1977) 1-65. MR 58:18570
    • (1977) Russ. Math. Surveys , vol.32 , Issue.6 , pp. 1-65
    • Nekhoroshev, N.N.1
  • 66
    • 84990623105 scopus 로고
    • Integrability of Hamiltonian systems on Cantor sets
    • MR 84d:58039
    • J. Pöschel, Integrability of Hamiltonian systems on Cantor sets, Comm. Pure Appl. Math. 35(5) (1982) 653-696. MR 84d:58039
    • (1982) Comm. Pure Appl. Math. , vol.35 , Issue.5 , pp. 653-696
    • Pöschel, J.1
  • 67
    • 0000882204 scopus 로고
    • On elliptic lower dimensional tori in Hamiltonian systems
    • MR 91a:58065
    • J. Pöschel, On elliptic lower dimensional tori in Hamiltonian systems, Math. Z. 202 (1989) 559-608. MR 91a:58065
    • (1989) Math. Z. , vol.202 , pp. 559-608
    • Pöschel, J.1
  • 68
    • 2342497628 scopus 로고    scopus 로고
    • A lecture on the classical KAM theorem
    • A. Katok et al., eds., Proceedings of Symposia in Pure Mathematics MR 2002g:37081
    • J. Pöschel. A lecture on the classical KAM theorem. In A. Katok et al., eds., Proceedings of Symposia in Pure Mathematics 69. Amer. Math. Soc. (2001), 707-732. MR 2002g:37081
    • (2001) Amer. Math. Soc. , vol.69 , pp. 707-732
    • Pöschel, J.1
  • 71
    • 34250451946 scopus 로고
    • On the nature of turbulence
    • D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20 (1971) 167-192; 23 (1971) 343-4. MR 44:1297
    • (1971) Commun. Math. Phys. , vol.20 , pp. 167-192
    • Ruelle, D.1    Takens, F.2
  • 72
    • 0345792509 scopus 로고
    • MR 44:1297
    • D. Ruelle and F. Takens, On the nature of turbulence, Commun. Math. Phys. 20 (1971) 167-192; 23 (1971) 343-4. MR 44:1297
    • (1971) Commun. Math. Phys. , vol.23 , pp. 343-344
  • 73
    • 13844308099 scopus 로고
    • Konvergente Reihenentwicklungen in der Störungstheorie der Himmelsmechanik
    • K. Jacobs (ed.), Heidelberger Taschenbücher Springer Verlag. MR 82j:70011
    • H. Rüssmann, Konvergente Reihenentwicklungen in der Störungstheorie der Himmelsmechanik. In K. Jacobs (ed.), Selecta Mathematica V, Heidelberger Taschenbücher 201 (1979) 93-260, Springer Verlag. MR 82j:70011
    • (1979) Selecta Mathematica V , vol.201 , pp. 93-260
    • Rüssmann, H.1
  • 74
    • 0347986631 scopus 로고
    • New results in the reversible KAM theory
    • S.B. Kuksin, V.F. Lazutkin and J. Pöschel (eds.), St. Petersburg, Birkhäuser 1994. MR 96d:58120
    • M.B. Sevryuk, New results in the reversible KAM theory. In: S.B. Kuksin, V.F. Lazutkin and J. Pöschel (eds.), Seminar on Dynamical Systems (St. Petersburg, 1991) 184-199, Birkhäuser 1994. MR 96d:58120
    • (1991) Seminar on Dynamical Systems , pp. 184-199
    • Sevryuk, M.B.1
  • 75
    • 0000595016 scopus 로고
    • Iteration of analytic functions
    • MR 4:76c
    • C.L. Siegel, Iteration of analytic functions, Ann. of Math. (2) 43 (1942) 607-612. MR 4:76c
    • (1942) Ann. of Math. (2) , vol.43 , pp. 607-612
    • Siegel, C.L.1
  • 76
    • 84968499117 scopus 로고
    • Differentiable functions defined in closed sets
    • H. Whitney, Differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36(2) (1934) 369-387.
    • (1934) Trans. Amer. Math. Soc. , vol.36 , Issue.2 , pp. 369-387
    • Whitney, H.1
  • 77
    • 13844319902 scopus 로고
    • 1-conjugaisons des difféomorphismes du cercle
    • J. Palis (ed), Proceedings, Rio de Janeiro 1981, LNM MR 85h:58102
    • 1-conjugaisons des difféomorphismes du cercle. In: J. Palis (ed), Geometric Dynamics, Proceedings, Rio de Janeiro 1981, LNM 1007 (1983) 814-827. MR 85h:58102
    • (1983) Geometric Dynamics , vol.1007 , pp. 814-827
    • Yoccoz, J.-C.1
  • 78
    • 0002419165 scopus 로고
    • Théorème de Siegel, nombres de Bruno et polynômes quadratiques
    • MR 96m:58214
    • J.-C. Yoccoz, Théorème de Siegel, nombres de Bruno et polynômes quadratiques, Astérisque 231 (1995) 3-88. MR 96m:58214
    • (1995) Astérisque , vol.231 , pp. 3-88
    • Yoccoz, J.-C.1
  • 79
    • 2942654549 scopus 로고    scopus 로고
    • Analytic linearization of circle diffeomorphisms
    • S. Marmi, L.H. Eliasson, S.B. Kuksin and J.-C. Yoccoz (eds.), LNM Springer Verlag
    • J.-C. Yoccoz, Analytic linearization of circle diffeomorphisms. In: S. Marmi, L.H. Eliasson, S.B. Kuksin and J.-C. Yoccoz (eds.), Dynamical Systems and Small Divisors, LNM 1784 (2002) 125-174, Springer Verlag.
    • (2002) Dynamical Systems and Small Divisors , vol.1784 , pp. 125-174
    • Yoccoz, J.-C.1
  • 80
    • 84968516185 scopus 로고
    • An implicit function theorem for small divisor problems
    • MR 49:4019
    • E. Zehnder, An implicit function theorem for small divisor problems, Bull. Amer. Math. Soc. 80(1) (1974) 174-179. MR 49:4019
    • (1974) Bull. Amer. Math. Soc. , vol.80 , Issue.1 , pp. 174-179
    • Zehnder, E.1
  • 81
    • 84980189959 scopus 로고
    • Generalized implicit function theorems with applications to some small divisor problems, I and II
    • E. Zehnder, Generalized implicit function theorems with applications to some small divisor problems, I and II, Comm. Pure Appl. Math. 28(1) (1975) 91-140; 29(1) (1976) 49-111. MR 54:14001
    • (1975) Comm. Pure Appl. Math. , vol.28 , Issue.1 , pp. 91-140
    • Zehnder, E.1
  • 82
    • 84980189959 scopus 로고
    • MR 54:14001
    • E. Zehnder, Generalized implicit function theorems with applications to some small divisor problems, I and II, Comm. Pure Appl. Math. 28(1) (1975) 91-140; 29(1) (1976) 49-111. MR 54:14001
    • (1976) Comm. Pure Appl. Math. , vol.29 , Issue.1 , pp. 49-111


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