I moti quasi periodici e la stabilità del sistema solare. II: Dai tori di Kolmogorov alla stabilità esponenziale
Giorgilli, Antonio
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 465-495 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)
Publié le : 2007-12-01
@article{BUMI_2007_8_10A_3_465_0,
     author = {Antonio Giorgilli},
     title = {I moti quasi periodici e la stabilit\`a del sistema solare.  II: Dai tori di Kolmogorov alla stabilit\`a esponenziale},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {465-495},
     mrnumber = {2394380},
     language = {it},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10A_3_465_0}
}

Giorgilli, Antonio. I moti quasi periodici e la stabilità del sistema solare.  II: Dai tori di Kolmogorov alla stabilità esponenziale. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 465-495. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10A_3_465_0/

[1] 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, 13 (1963); Russ. Math. Surv., 18 (1963), 9. | MR 163025

[2] Arnold, V. I., 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. | MR 170705

[3] Arnold, V. I., Instability of dynamical systems with several degrees of freedom, Sov. Math. Dokl., 5 N. 1 (1964), 581-585. | Zbl 0135.42602

[4] Benettin, G. - Galgani, L. - Giorgilli, A. - Strelcyn, J. M., Tous les nombres characteristiques de Ljapunov sont effectivement calculables, C. R. Acad. Sc. Paris 268 A (1978), 431-433. | MR 516345 | Zbl 0374.65046

[5] Benettin, G. - Galgani, L. - Giorgilli, A. - Strelcyn, J. M., Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them, part 1: theory, Meccanica (1980), 9-20; Part 2: numerical applications, Meccanica (1980), 21-30. | Zbl 0488.70015

[6] Benettin, G. - Galgani, L. - Giorgilli, A., A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems. Cel. Mech., 37 (1985), 1-25. | MR 830795 | Zbl 0602.58022

[7] Benettin, G. - Gallavotti, G., Stability of motions near resonances in quasi- integrable Hamiltonian systems. Journ. Stat. Phys., 44 (1986), 293. | MR 857061 | Zbl 0636.70018

[8] Birkhoff, G. D., Dynamical systems, New York (1927). | MR 209095

[9] Carpino, M. - Milani, A. - Nobili, A., Long term numerical integration and synthetic theories for the motion of outer planets, Astronomy and Astrophysics, 181 (1987), 182-194. | Zbl 0618.70006

[10] Celletti, A. - Chierchia, L., KAM stability and Celestial Mechanics, Memoirs of AMS, 187 n. 878 (2007). | MR 2307840

[11] Contopoulos, G., Order and chaos in dynamical Astronomy, Springer-Verlag (2002). | MR 1988785 | Zbl 1041.85001

[12] Efthimiopoulos, C. - Sandor, Z., Optimized Nekhoroshev stability estimates for the Trojan asteroids with a symplectic mapping model of co-orbital motion, Mon. Not. R. Astron. Soc., (2005).

[13] Fermi, E. - Pasta, J. - Ulam, S., Studies of nonlinear problems, Los Alamos document LA-1940 (1955). | Zbl 0353.70028

[14] Giorgilli, A. - Zehnder, E., Exponential stability for time dependent potentials, ZAMP (1992). | MR 1182784 | Zbl 0766.58032

[15] Giorgilli, A. - Skokos, Ch., On the stability of the Trojan asteroids, Astron. Astroph., 317 (1997), 254-261.

[16] Giorgilli, A., Notes on exponential stability of Hamiltonian systems, in Dynamical Systems, Part I: Hamiltonian systems and Celestial MechanicsPubblicazioni del Centro di Ricerca Matematica Ennio De Giorgi, Pisa (2003), 87-198. | MR 2071233 | Zbl 1081.37033

[17] Gustavson, F. G., On constructing formal integrals of a Hamiltonian system near an equilibrium point, Astron. J., 71 (1966), 670-686.

[18] Henon, M. - Heiles, C., The applicability of the third integral of motion: some numerical experiments, Astron. J., 69 (1964), 73-79. | MR 158746

[19] Kirkwood, D., Proceedings of the American Association for the Advancement of Science for 1866. | MR 1568920

[20] Kirkwood, D., The zone of asteroids and the ring of Saturn, Astronomical Register, 22 (1884), 243-247.

[21] Kolmogorov, A. N., Preservation of conditionally periodic movements with small change in the Hamilton function, Dokl. Akad. Nauk SSSR, 98 (1954), 527. | MR 68687 | Zbl 0056.31502

[22] Laskar, J., A numerical experiment on the chaotic behaviour of the solar system, Nature, 338 (1989), 237-238.

[23] Laskar, J., Large scale chaos in the solar system, Astron. Astroph., 287 (1994). | Zbl 1052.70547

[24] Littlewood, J. E., On the equilateral configuration in the restricted problem of three bodies, Proc. London Math. Soc. (3) 9 (1959), 343-372. | MR 109077 | Zbl 0092.16802

[25] Littlewood, J. E., The Lagrange configuration in celestial mechanics, Proc. London Math. Soc. (3) 9 (1959), 525-543. | MR 1576803 | Zbl 0093.17302

[26] Locatelli, U. - Giorgilli, A., Invariant tori in the Sun-Jupiter-Saturn system, DCDS-B, 7 (2007), 377-398. | MR 2276414 | Zbl 1129.70015

[27] Lochak, P., Canonical perturbation theory via simultaneous approximations, Usp. Math. Nauk.47 (1992), 59-140. English transl in Russ. Math. Surv. | MR 1209145 | Zbl 0795.58042

[28] Milani, A. - Nobili, A. - Carpino, M., Secular variations of the semimajor axes: theory and experiments, Astronomy and Astrophysics, 172 (1987), 265-269. | Zbl 0617.70009

[29] Moltchanov, A., The resonant structure of the solar system, Icarus8 (1968), 203-215.

[30] Morbidelli, A. - Giorgilli, A., On the dynamics in the asteroids' belt. Part I: general theory, Cel. Mech. 47 (1990), 145-172. | MR 1050337 | Zbl 0701.70010

[31] Morbidelli, A. - Giorgilli, A., On the dynamics in the asteroids' belt. Part II: detailed study of the main resonances, Cel. Mech., 47 (1990), 173-204. | MR 1050338 | Zbl 0701.70011

[32] Morbidelli, A. - Giorgilli, A., Superexponential stability of KAM tori, J. Stat. Phys., 78 (1995), 1607-1617. | MR 1316113

[33] Morbidelli, A., Modern celestial Mechanics. Aspects of solar system dynamics, Taylor & Francis, London (2002).

[34] Moser, J., Stabilitätsverhalten kanonisher differentialgleichungssysteme, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl IIa, nr. 6 (1955), 87-120.

[35] Moser, J., On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl II (1962), 1-20. | Zbl 0107.29301

[36] Moser, J., Stable and random motions in dynamical systems, Princeton University press, Princeton (1973). | Zbl 0271.70009

[37] Murray, N. - Holman, M., The Origin of Chaos in Outer Solar System, Science, 283, Iss. 5409, 1877 (1999).

[38] Nekhoroshev, N. N., Exponential estimates of the stability time of near-integrable Hamiltonian systems. Russ. Math. Surveys, 32 (1977), 1. | Zbl 0389.70028

[39] Nekhoroshev, N. N., Exponential estimates of the stability time of near-integrable Hamiltonian systems, 2. Trudy Sem. Petrovs., 5 (1979), 5.

[40] Robutel, P. - Gabern, F. - Jorba, A., The observed Trojans and the global dynamics around the Lagrangian points of the Sun-Jupiter system, Celest. Mech. Dyn. Astr., 92 (2005), 53-69. | Zbl 1083.70019

[41] Roels, J. - Hnon, M., Recherche des courbes invariantes d'une transformation ponctuelle plane conservant les aires, Bull. Astron., 32 (1967), 267-285. | Zbl 0171.22902

[42] Sussman, G. J. - Wisdom, J., Numerical evidence that the motion of Pluto is chaotic, Science, 241 (1988), 433-437.