메뉴 건너뛰기




Volumn 10, Issue 2, 2005, Pages 153-171

Construction of Kolmogorov's normal form for a planetary system

Author keywords

Celestial mechanics; Hamiltonian systems; KAM theory; n body problem; Perturbation methods; Three body problem

Indexed keywords


EID: 33645577452     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2005v010n02ABEH000309     Document Type: Article
Times cited : (22)

References (30)
  • 1
    • 0141781369 scopus 로고    scopus 로고
    • On a strange resonance noticed by M. Herman
    • K. Abdullah, A. Albouy. On a strange resonance noticed by M. Herman. Reg. & Chaot. Dyn. 2001. V. 6. No4. P. 421-432.
    • (2001) Reg. & Chaot. Dyn. , vol.6 , Issue.4 , pp. 421-432
    • Abdullah, K.1    Albouy, A.2
  • 2
    • 0002764805 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. 1963. V. 18. No13.
    • (1963) Usp. Mat. Nauk. , vol.18 , Issue.13
    • Arnold, V.I.1
  • 3
    • 0348094266 scopus 로고
    • Russ. Math. Surv. 1963. V. 18. P. 9-36.
    • (1963) Russ. Math. Surv. , vol.18 , pp. 9-36
  • 4
    • 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. Usp. Math. Nauk. 1963. V. 18. No6. P. 91.
    • (1963) Usp. Math. Nauk. , vol.18 , Issue.6 , pp. 91
    • Arnold, V.I.1
  • 5
    • 0002356196 scopus 로고
    • Russ. Math. Surv. 1963. V. 18. No6. p. 85.
    • (1963) Russ. Math. Surv. , vol.18 , Issue.6 , pp. 85
  • 7
    • 33645566762 scopus 로고    scopus 로고
    • On the breakdown threshold of invariant tori in four dimensional maps
    • A. Celletti, C. Falcolini, U. Locatelli. On the breakdown threshold of invariant tori in four dimensional maps. Reg. & Chaot. Dyn. 2004. V. 9. No3. P. 227-253.
    • (2004) Reg. & Chaot. Dyn. , vol.9 , Issue.3 , pp. 227-253
    • Celletti, A.1    Falcolini, C.2    Locatelli, U.3
  • 9
    • 9444295902 scopus 로고    scopus 로고
    • Démonstration du "théorème d'Arnold" sur la stabilité du système planétaire (d'après Michael Herman)
    • J. Fejoz. Démonstration du "théorème d'Arnold" sur la stabilité du système planétaire (d'après Michael Herman). Ergodic Theory Dyn. Sys. 2004. V. 24. No5. P. 1521-1582.
    • (2004) Ergodic Theory Dyn. Sys. , vol.24 , Issue.5 , pp. 1521-1582
    • Fejoz, J.1
  • 10
    • 21244477875 scopus 로고    scopus 로고
    • On the construction of the Kolmogorov normal form for the Trojan asteroids
    • F. Gabern, A. Jorba, U. Locatelli. On the construction of the Kolmogorov normal form for the Trojan asteroids. Nonlinearity. 2005. V. 18. No4. p. 1705-1734.
    • (2005) Nonlinearity , vol.18 , Issue.4 , pp. 1705-1734
    • Gabern, F.1    Jorba, A.2    Locatelli, U.3
  • 13
  • 14
    • 0001246972 scopus 로고
    • Preservation of conditionally periodic movements with small change in the Hamilton function
    • A. N. Kolmogorov. Preservation of conditionally periodic movements with small change in the Hamilton function. Dokl. Akad. Nauk SSSR. 1954. V. 98. P. 527-530.
    • (1954) Dokl. Akad. Nauk SSSR , vol.98 , pp. 527-530
    • Kolmogorov, A.N.1
  • 15
    • 0009169213 scopus 로고
    • Engl. transl. in: G. Casati, J. Ford (eds.)
    • (Engl. transl. in: G. Casati, J. Ford (eds.). Lecture Notes in Physics. 1979. No93. P. 51-56)
    • (1979) Lecture Notes in Physics , Issue.93 , pp. 51-56
  • 16
    • 0041484625 scopus 로고
    • Groupe de travail sur la lecture des Méthodes nouvelles de la Mécanique Céleste. Notes scientifiques et techniques du Bureau des Longitudes S026
    • J. Laskar. Les variables de Poincaré et le développement de la fonction perturbatrice. Groupe de travail sur la lecture des Méthodes nouvelles de la Mécanique Céleste. Notes scientifiques et techniques du Bureau des Longitudes S026. 1989.
    • (1989) Les Variables de Poincaré et Le Développement de la Fonction Perturbatrice
    • Laskar, J.1
  • 18
    • 0001192298 scopus 로고
    • A numerical experiment on the chaotic behaviour of the solar system
    • J. Laskar. A numerical experiment on the chaotic behaviour of the solar system. Nature. 1989. V. 338. P. 237-238.
    • (1989) Nature , vol.338 , pp. 237-238
    • Laskar, J.1
  • 19
    • 0346001036 scopus 로고    scopus 로고
    • Large scale chaos and marginal stability in the solar system
    • J. Laskar. Large scale chaos and marginal stability in the solar system. Celestial Mechanics and Dynamical Astronomy. 1996. V. 64. P. 115-162.
    • (1996) Celestial Mechanics and Dynamical Astronomy , vol.64 , pp. 115-162
    • Laskar, J.1
  • 21
    • 0013366568 scopus 로고    scopus 로고
    • High order symplectic integrators for perturbed Hamiltonian systems
    • J. Laskar, P,. Robutel. High order symplectic integrators for perturbed Hamiltonian systems. Celestial Mechanics and Dynamical Astronomy. 2001. V. 80. P. 39-62.
    • (2001) Celestial Mechanics and Dynamical Astronomy , vol.80 , pp. 39-62
    • Laskar, J.1    Robutel, P.2
  • 22
    • 0042728523 scopus 로고    scopus 로고
    • Invariant tori in the secular motions of the three-body planetary systems
    • U. Locatelli, A. Giorgilli. Invariant tori in the secular motions of the three-body planetary systems. Celestial Mechanics and Dynamical Astronomy. 2000. V. 78. P. 47-74.
    • (2000) Celestial Mechanics and Dynamical Astronomy , vol.78 , pp. 47-74
    • Locatelli, U.1    Giorgilli, A.2
  • 23
    • 0036388310 scopus 로고    scopus 로고
    • Partial reduction in the N-body planetary problem using the angular momentum integral
    • F. Malige, P. Robutel, J. Laskar. Partial reduction in the N-body planetary problem using the angular momentum integral. Celestial Mechanics and Dynamical Astronomy. 2002. V. 84. P. 283-316.
    • (2002) Celestial Mechanics and Dynamical Astronomy , vol.84 , pp. 283-316
    • Malige, F.1    Robutel, P.2    Laskar, J.3
  • 24
    • 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. K1 1962. V. 1962. P. 1-20.
    • (1962) Nachr. Akad. Wiss. Gött., II Math. Phys. K1 , vol.1962 , pp. 1-20
    • Moser, J.1
  • 25
    • 0033583234 scopus 로고    scopus 로고
    • The origin of chaos in outer solar system
    • N. Murray, M. Holman. The Origin of Chaos in Outer Solar System. Science. 1999. V. 283. Iss. 5409. P. 1877-....
    • (1999) Science , vol.283 , Issue.5409 , pp. 1877
    • Murray, N.1    Holman, M.2
  • 29
    • 0042682409 scopus 로고
    • Stability of the planetary three-body problem - II. KAM theory and existence of quasiperiodic motions
    • P. Robutel. Stability of the Planetary Three-Body Problem - II. KAM Theory and Existence of Quasiperiodic Motions. Celestial Mechanics and Dynamical Astronomy. 1995. V. 62. P. 219-261.
    • (1995) Celestial Mechanics and Dynamical Astronomy , vol.62 , pp. 219-261
    • Robutel, P.1
  • 30
    • 0001348025 scopus 로고
    • Numerical evidence that the motion of Pluto is chaotic
    • G. J. Sussman, J. Wisdom. Numerical evidence that the motion of Pluto is chaotic. Science. 1988. V. 241. P. 433-437.
    • (1988) Science , vol.241 , pp. 433-437
    • Sussman, G.J.1    Wisdom, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.