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Volumn 48, Issue 2, 1997, Pages 220-261

Kolmogorov theorem and classical perturbation theory

Author keywords

Hamiltonian perturbations; KAM theory; Quasiperiodic motion

Indexed keywords


EID: 0031475863     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00001475     Document Type: Article
Times cited : (36)

References (23)
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  • 3
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  • 4
    • 0002341745 scopus 로고
    • Über die Normalformen analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung
    • C. L. Siegel, Über die Normalformen analytischer Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Nachr. Acad. Wiss. Göttingen, Math. Phys. Kl, IIA (1952) 21-30.
    • (1952) Nachr. Acad. Wiss. Göttingen, Math. Phys. Kl , vol.IIA , pp. 21-30
    • Siegel, C.L.1
  • 5
    • 0001851184 scopus 로고
    • On invariant curves of area-preserving mappings of an annulus
    • J. Moser, On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Gött., II Math. Phys. Kl 1962 (1962), 1-20.
    • (1962) Nachr. Akad. Wiss. Gött., II Math. Phys. Kl , vol.1962 , pp. 1-20
    • Moser, J.1
  • 6
    • 3042570326 scopus 로고
    • Convergent series expansions for quasi-periodic motions
    • J. Moser, Convergent series expansions for quasi-periodic motions, Math. Ann. 169 (1967), 136-176.
    • (1967) Math. Ann. , vol.169 , pp. 136-176
    • Moser, J.1
  • 7
    • 0002764803 scopus 로고
    • Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian
    • V. I. Arnold, Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian, Usp. Mat. Nauk 18 (1963), 13; Russ. Math. Surv. 18 (1963), 9.
    • (1963) Usp. Mat. Nauk , vol.18 , pp. 13
    • Arnold, V.I.1
  • 8
    • 0040302033 scopus 로고
    • V. I. Arnold, Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian, Usp. Mat. Nauk 18 (1963), 13; Russ. Math. Surv. 18 (1963), 9.
    • (1963) Russ. Math. Surv. , vol.18 , pp. 9
  • 9
    • 0002356198 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, Usp. Math. Nauk 18 N.6 (1963), 91; Russ. Math. Surv. 18 N.6 (1963), 85.
    • (1963) Usp. Math. Nauk , vol.18 , Issue.6 , pp. 91
    • Arnold, V.I.1
  • 10
    • 0002356196 scopus 로고
    • V. I. Arnold, Small denominators and problems of stability of motion in classical and celestial mechanics, Usp. Math. Nauk 18 N.6 (1963), 91; Russ. Math. Surv. 18 N.6 (1963), 85.
    • (1963) Russ. Math. Surv. , vol.18 , Issue.6 , pp. 85
  • 12
    • 3042561484 scopus 로고    scopus 로고
    • Absolutely convergent series expansion for quasi-periodic motions
    • report 2-88, Dept. of Math., Univ. of Stockholm (1988), now published in paper 4
    • L. H. Eliasson, Absolutely convergent series expansion for quasi-periodic motions, report 2-88, Dept. of Math., Univ. of Stockholm (1988), now published in MPEJ 2, paper 4 (1996).
    • (1996) MPEJ , vol.2
    • Eliasson, L.H.1
  • 15
    • 0000446018 scopus 로고
    • Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable Hamiltonian systems. A review
    • G. Gallavotti, Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable Hamiltonian systems. A review, Reviews in Math. Phys. 6 (1994), 343-411.
    • (1994) Reviews in Math. Phys. , vol.6 , pp. 343-411
    • Gallavotti, G.1
  • 16
    • 21344496040 scopus 로고
    • Twistless KAM tori
    • G. Gallavotti, Twistless KAM tori, Comm. Math. Phys. 164 (1994), 145-156.
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    • Gallavotti, G.1
  • 22
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    • On the one-dimensional Schrödinger equation with a quasi-periodic potential
    • H. Rüssmann, On the one-dimensional Schrödinger equation with a quasi-periodic potential, Ann. New York Acad. Sci. 357 (1980), 90-107.
    • (1980) Ann. New York Acad. Sci. , vol.357 , pp. 90-107
    • Rüssmann, H.1
  • 23
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    • Exponential stability for time dependent potentials
    • A. Giorgilli and E. Zehnder, Exponential stability for time dependent potentials, ZAMP 43 (1992), 827-855.
    • (1992) ZAMP , vol.43 , pp. 827-855
    • Giorgilli, A.1    Zehnder, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.