메뉴 건너뛰기




Volumn 7, Issue 2, 2007, Pages 377-398

Invariant tori in the Sun-Jupiter-Saturn system

Author keywords

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

Indexed keywords


EID: 34247209662     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2007.7.377     Document Type: Article
Times cited : (32)

References (31)
  • 1
    • 0002764805 scopus 로고
    • Proof of a theorem of A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian
    • Arnold, V. I., 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);
    • (1963) Usp. Mat. Nauk , vol.18
    • Arnold, V.I.1
  • 2
    • 0348094266 scopus 로고
    • Russ. Math. Surv., 18 (1963), 9-36 .
    • (1963) Russ. Math. Surv , vol.18 , pp. 9-36
  • 3
    • 0002356196 scopus 로고
    • Small denominators and problems of stability of motion in classical and celestial mechanics
    • Arnold, V. I., Small denominators and problems of stability of motion in classical and celestial mechanics, Usp. Math. Nauk 18 (1963) 91;
    • (1963) Usp. Math. Nauk , vol.18 , pp. 91
    • Arnold, V.I.1
  • 4
    • 0002356196 scopus 로고
    • Russ. Math. Surv., 18 (1963), 85.
    • (1963) Russ. Math. Surv , vol.18 , pp. 85
  • 5
    • 0012523582 scopus 로고
    • Théorie générale du couple Jupiter- Saturne par une méthode iterative
    • Bretagnon, P. and Simon, J.-L., Théorie générale du couple Jupiter- Saturne par une méthode iterative, Astronomy and Astrophysics, 239 (1990), 387-398.
    • (1990) Astronomy and Astrophysics , vol.239 , pp. 387-398
    • Bretagnon, P.1    Simon, J.-L.2
  • 6
    • 39749092926 scopus 로고    scopus 로고
    • KAM stability and Celestial Mechanics
    • in press
    • Celletti, A., Chierchia, L., KAM stability and Celestial Mechanics, Memoirs of AMS, in press 2005.
    • (2005) Memoirs of AMS
    • Celletti, A.1    Chierchia, L.2
  • 7
    • 33645566762 scopus 로고    scopus 로고
    • On the break-down threshold of invariant tort in four dimensional maps
    • Celletti, A., Falcolini, C. and Locatelli, U., On the break-down threshold of invariant tort in four dimensional maps, Regular and Chaotic Dynamics, 9 (2004), 227-253.
    • (2004) Regular and Chaotic Dynamics , vol.9 , pp. 227-253
    • Celletti, A.1    Falcolini, C.2    Locatelli, U.3
  • 8
    • 33749333014 scopus 로고
    • Rigorous numerical stability estimates for the existence of KAM tori in a forced pendulum
    • Celletti, A., Falcolini, C. and Porzio, A., Rigorous numerical stability estimates for the existence of KAM tori in a forced pendulum, Ann. Inst, H. Poincare', 47 (1987), 85-111.
    • (1987) Ann. Inst, H. Poincare , vol.47 , pp. 85-111
    • Celletti, A.1    Falcolini, C.2    Porzio, A.3
  • 9
    • 9444295902 scopus 로고    scopus 로고
    • Démonstration du "théorème d'Arnold" sur la stabilité du système planétaire (d'après Michael Herman)
    • Fejoz, J., Démonstration du "théorème d'Arnold" sur la stabilité du système planétaire (d'après Michael Herman), Ergodic Theory Dyn. Sys., 24, 1521- 1582.
    • Ergodic Theory Dyn. Sys , vol.24 , pp. 1521-1582
    • Fejoz, J.1
  • 10
    • 21244477875 scopus 로고    scopus 로고
    • On the construction of the Kolmogorov normal form for the Trojan asteroids
    • Gabern, F., Jorba, A. and Locatelli, U., On the construction of the Kolmogorov normal form for the Trojan asteroids, Nonlinearity, 18 (2005), 1705-1734.
    • (2005) Nonlinearity , vol.18 , pp. 1705-1734
    • Gabern, F.1    Jorba, A.2    Locatelli, U.3
  • 11
    • 34247270807 scopus 로고    scopus 로고
    • Giorgilli, A., Quantitative methods in classical perturbation theory, proceedings of the Nato ASI school From Newton to chaos, modern techniques for understanding and coping with chaos in N-body dynamical systems, A.B. Roy e B.D. Steves eds., Plenum Press, New York 1995.
    • Giorgilli, A., Quantitative methods in classical perturbation theory, proceedings of the Nato ASI school "From Newton to chaos, modern techniques for understanding and coping with chaos in N-body dynamical systems", A.B. Roy e B.D. Steves eds., Plenum Press, New York 1995.
  • 12
    • 34247212802 scopus 로고    scopus 로고
    • Giorgilli., A., Notes on exponential stability of Hamiltonian systems in Dynamical systems, Part I. Pubbl. Cent. Ric. Mat. Ennio De Giorgi, Scuola Norm. Sup., Pisa, 87- 198 2003.
    • Giorgilli., A., Notes on exponential stability of Hamiltonian systems in "Dynamical systems," Part I. Pubbl. Cent. Ric. Mat. Ennio De Giorgi, Scuola Norm. Sup., Pisa, 87- 198 2003.
  • 13
    • 0031475863 scopus 로고    scopus 로고
    • Giorgilli, A. and Locatelli, U., Kolmogorov theorem and classical perturbation theory, 3. of App. Math, and Phys. (ZAMP), 48 (1997), 220-261.
    • Giorgilli, A. and Locatelli, U., Kolmogorov theorem and classical perturbation theory, 3. of App. Math, and Phys. (ZAMP), 48 (1997), 220-261.
  • 14
    • 0040217575 scopus 로고    scopus 로고
    • On classical series expansion for quasi- periodic motions
    • Giorgilli, A. and Locatelli, U., On classical series expansion for quasi- periodic motions, MPEJ, 3 (1997), 1-25.
    • (1997) MPEJ , vol.3 , pp. 1-25
    • Giorgilli, A.1    Locatelli, U.2
  • 15
    • 0001246972 scopus 로고
    • Preservation of conditionally periodic movements with small change in the Hamilton function
    • Kolmogorov, A. N., Preservation of conditionally periodic movements with small change in the Hamilton function, Dokl. Akad. Nauk SSSR, 98 (1954), 527-530;
    • (1954) Dokl. Akad. Nauk SSSR , vol.98 , pp. 527-530
    • Kolmogorov, A.N.1
  • 16
    • 0009169213 scopus 로고
    • and, eds
    • engl. transl. in Casati, G. and Ford, J. (eds.), Lecture Notes in Physics, 93 (1979), 51-56.
    • (1979) Lecture Notes in Physics , vol.93 , pp. 51-56
    • engl1    transl2
  • 17
    • 34247208085 scopus 로고    scopus 로고
    • Laskar, J., Systèmes de variables et élé ments, in Les Méthodes modernes de la Mécanique Céleste (eds, Benest, D. and Froeschlé, C. ), 63-87, Editions Frontières 1989.
    • Laskar, J., Systèmes de variables et élé ments, in "Les Méthodes modernes de la Mécanique Céleste" (eds, Benest, D. and Froeschlé, C. ), 63-87, Editions Frontières 1989.
  • 18
    • 0001192298 scopus 로고
    • A numerical experiment on the chaotic behaviour of the solar system
    • Laskar, J., A numerical experiment on the chaotic behaviour of the solar system, Nature, 338 (1989), 237-238.
    • (1989) Nature , vol.338 , pp. 237-238
    • Laskar, J.1
  • 19
    • 34247278186 scopus 로고    scopus 로고
    • Laskar, J., Introduction to frequency map analysis, in Proceedings of the NATO ASI school, Hamiltonian Systems with Three or More Degrees of Freedom (managing ed. C. Simò), (1999) 134-150, S'Agaro (Spain), Kluwer, 1995.
    • Laskar, J., Introduction to frequency map analysis, in Proceedings of the NATO ASI school, "Hamiltonian Systems with Three or More Degrees of Freedom" (managing ed. C. Simò), (1999) 134-150, S'Agaro (Spain), Kluwer, 1995.
  • 20
    • 33751077602 scopus 로고    scopus 로고
    • Frequency Map analysis and quasi periodic decompositions
    • eds. Benest, D, Froeschlé, C. and Lega E, Taylor and Francis, in press
    • Laskar, J , Frequency Map analysis and quasi periodic decompositions, in "Hamiltonian Systems and Fourier Analysis" (eds. Benest, D., Froeschlé, C. and Lega E.), Taylor and Francis, in press.
    • Hamiltonian Systems and Fourier Analysis
    • Laskar, J.1
  • 21
    • 0042096156 scopus 로고
    • Stability of the Planetary Three-Body Problem - I. Expansion of the Planetary Hamiltonian
    • Laskar, J. and Robutel, P., Stability of the Planetary Three-Body Problem - I. Expansion of the Planetary Hamiltonian, Celestial Mechanics and Dynamical Astronomy, 62 (1995), 193-217.
    • (1995) Celestial Mechanics and Dynamical Astronomy , vol.62 , pp. 193-217
    • Laskar, J.1    Robutel, P.2
  • 22
    • 0013366568 scopus 로고    scopus 로고
    • High order symplectic integrators for perturbed Hamiltonian systems
    • Laskar, J. and Robutel, P., High order symplectic integrators for perturbed Hamiltonian systems, Celestial Mechanics and Dynamical Astronomy, 80 (2001), 39-62.
    • (2001) Celestial Mechanics and Dynamical Astronomy , vol.80 , pp. 39-62
    • Laskar, J.1    Robutel, P.2
  • 23
    • 0042728523 scopus 로고    scopus 로고
    • Invariant tori in the secular motions of the three-body planetary systems
    • Locatelli, U. and Giorgilli, A., Invariant tori in the secular motions of the three-body planetary systems, Celestial Mechanics and Dynamical Astronomy, 78 (2000), 47- 74.
    • (2000) Celestial Mechanics and Dynamical Astronomy , vol.78 , pp. 47-74
    • Locatelli, U.1    Giorgilli, A.2
  • 24
    • 33645577452 scopus 로고    scopus 로고
    • Construction of the Kolmogorov's normal form for a planetary system
    • Locatelli, U. and Giorgilli, A., Construction of the Kolmogorov's normal form for a planetary system, Regular and Chaotic Dynamics, 10 (2005), 153-171.
    • (2005) Regular and Chaotic Dynamics , vol.10 , pp. 153-171
    • Locatelli, U.1    Giorgilli, A.2
  • 26
    • 0033583234 scopus 로고    scopus 로고
    • The Origin of Chaos in Outer Solar System
    • Murray, N. and Holman, M., The Origin of Chaos in Outer Solar System, Science, 283 (1999), 1877.
    • (1999) Science , vol.283 , pp. 1877
    • Murray, N.1    Holman, M.2
  • 30
    • 0042682409 scopus 로고
    • Stability of the Planetary Three-Body Problem - II. KAM Theory and Existence of Quasiperiodic Motions
    • Robutel, P., Stability of the Planetary Three-Body Problem - II. KAM Theory and Existence of Quasiperiodic Motions, Celestial Mechanics and Dynamical Astronomy, 62 (1995), 219-261.
    • (1995) Celestial Mechanics and Dynamical Astronomy , vol.62 , pp. 219-261
    • Robutel, P.1
  • 31
    • 0001348025 scopus 로고
    • Numerical evidence that the motion of Pluto is chaotic
    • Sussman, G.J. and Wisdom, J., Numerical evidence that the motion of Pluto is chaotic, Science, 241 (1988), 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.