bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

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 Serie 8 10-A (2007) —La Matematica nella Società e nella Cultura, fasc. n.3, p. 465-495, Unione Matematica Italiana (Italian)
Seguito di BUMI_2007_8_10A_1_55_0 | pdf (394 Kb), djvu (284 Kb). | MR 2394380

Referenze Bibliografiche
[1] 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, 13 (1963); Russ. Math. Surv., 18 (1963), 9. | MR 163025
[2] 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. | MR 170705
[3] V. I. ARNOLD, Instability of dynamical systems with several degrees of freedom, Sov. Math. Dokl., 5 N. 1 (1964), 581-585. | Zbl 0135.42602
[4] G. BENETTIN - L. GALGANI - A. GIORGILLI - J. M. STRELCYN, 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] G. BENETTIN - L. GALGANI - A. GIORGILLI - J. M. STRELCYN, 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] G. BENETTIN - L. GALGANI - A. GIORGILLI, A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems. Cel. Mech., 37 (1985), 1-25. | fulltext (doi) | MR 830795 | Zbl 0602.58022
[7] G. BENETTIN - G. GALLAVOTTI, Stability of motions near resonances in quasi- integrable Hamiltonian systems. Journ. Stat. Phys., 44 (1986), 293. | fulltext (doi) | MR 857061 | Zbl 0636.70018
[8] G. D. BIRKHOFF, Dynamical systems, New York (1927). | MR 209095
[9] M. CARPINO - A. MILANI - A. NOBILI, Long term numerical integration and synthetic theories for the motion of outer planets, Astronomy and Astrophysics, 181 (1987), 182-194. | Zbl 0618.70006
[10] A. CELLETTI - L. CHIERCHIA, KAM stability and Celestial Mechanics, Memoirs of AMS, 187 n. 878 (2007). | fulltext (doi) | MR 2307840
[11] G. CONTOPOULOS, Order and chaos in dynamical Astronomy, Springer-Verlag (2002). | fulltext (doi) | MR 1988785 | Zbl 1041.85001
[12] C. EFTHIMIOPOULOS - Z. SANDOR, Optimized Nekhoroshev stability estimates for the Trojan asteroids with a symplectic mapping model of co-orbital motion, Mon. Not. R. Astron. Soc., (2005).
[13] E. FERMI - J. PASTA - S. ULAM, Studies of nonlinear problems, Los Alamos document LA-1940 (1955). | Zbl 0353.70028
[14] A. GIORGILLI - E. ZEHNDER, Exponential stability for time dependent potentials, ZAMP (1992). | fulltext (doi) | MR 1182784 | Zbl 0766.58032
[15] A. GIORGILLI - Ch. SKOKOS, On the stability of the Trojan asteroids, Astron. Astroph., 317 (1997), 254-261.
[16] A. GIORGILLI, Notes on exponential stability of Hamiltonian systems, in Dynamical Systems, Part I: Hamiltonian systems and Celestial Mechanics Pubblicazioni del Centro di Ricerca Matematica Ennio De Giorgi, Pisa (2003), 87-198. | MR 2071233 | Zbl 1081.37033
[17] F. G. GUSTAVSON, On constructing formal integrals of a Hamiltonian system near an equilibrium point, Astron. J., 71 (1966), 670-686.
[18] M. HENON - C. HEILES, The applicability of the third integral of motion: some numerical experiments, Astron. J., 69 (1964), 73-79. | fulltext (doi) | MR 158746
[19] D. KIRKWOOD, Proceedings of the American Association for the Advancement of Science for 1866. | MR 1568920
[20] D. KIRKWOOD, The zone of asteroids and the ring of Saturn, Astronomical Register, 22 (1884), 243-247.
[21] A. N. KOLMOGOROV, 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] J. LASKAR, A numerical experiment on the chaotic behaviour of the solar system, Nature, 338 (1989), 237-238.
[23] J. LASKAR, Large scale chaos in the solar system, Astron. Astroph., 287 (1994). | Zbl 1052.70547
[24] J. E. LITTLEWOOD, On the equilateral configuration in the restricted problem of three bodies, Proc. London Math. Soc. (3) 9 (1959), 343-372. | fulltext (doi) | MR 109077 | Zbl 0092.16802
[25] J. E. LITTLEWOOD, The Lagrange configuration in celestial mechanics, Proc. London Math. Soc. (3) 9 (1959), 525-543. | fulltext (doi) | MR 1576803 | Zbl 0093.17302
[26] U. LOCATELLI - A. GIORGILLI, Invariant tori in the Sun-Jupiter-Saturn system, DCDS-B, 7 (2007), 377-398. | fulltext (doi) | MR 2276414 | Zbl 1129.70015
[27] P. LOCHAK, Canonical perturbation theory via simultaneous approximations, Usp. Math. Nauk. 47 (1992), 59-140. English transl in Russ. Math. Surv. | fulltext (doi) | MR 1209145 | Zbl 0795.58042
[28] A. MILANI - A. NOBILI - M. CARPINO, Secular variations of the semimajor axes: theory and experiments, Astronomy and Astrophysics, 172 (1987), 265-269. | Zbl 0617.70009
[29] A. MOLTCHANOV, The resonant structure of the solar system, Icarus 8 (1968), 203-215.
[30] A. MORBIDELLI - A. GIORGILLI, On the dynamics in the asteroids' belt. Part I: general theory, Cel. Mech. 47 (1990), 145-172. | fulltext (doi) | MR 1050337 | Zbl 0701.70010
[31] A. MORBIDELLI - A. GIORGILLI, On the dynamics in the asteroids' belt. Part II: detailed study of the main resonances, Cel. Mech., 47 (1990), 173-204. | fulltext (doi) | MR 1050338 | Zbl 0701.70011
[32] A. MORBIDELLI - A. GIORGILLI, Superexponential stability of KAM tori, J. Stat. Phys., 78 (1995), 1607-1617. | fulltext (doi) | MR 1316113
[33] A. MORBIDELLI, Modern celestial Mechanics. Aspects of solar system dynamics, Taylor & Francis, London (2002).
[34] J. MOSER, Stabilitätsverhalten kanonisher differentialgleichungssysteme, Nachr. Akad. Wiss. Göttingen, Math. Phys. Kl IIa, nr. 6 (1955), 87-120.
[35] J. MOSER, 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] J. MOSER, Stable and random motions in dynamical systems, Princeton University press, Princeton (1973). | Zbl 0271.70009
[37] N. MURRAY - M. HOLMAN, The Origin of Chaos in Outer Solar System, Science, 283, Iss. 5409, 1877 (1999).
[38] N. N. NEKHOROSHEV, Exponential estimates of the stability time of near-integrable Hamiltonian systems. Russ. Math. Surveys, 32 (1977), 1. | Zbl 0389.70028
[39] N. N. NEKHOROSHEV, Exponential estimates of the stability time of near-integrable Hamiltonian systems, 2. Trudy Sem. Petrovs., 5 (1979), 5.
[40] P. ROBUTEL - F. GABERN - A. JORBA, 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] J. ROELS - M. HNON, Recherche des courbes invariantes d'une transformation ponctuelle plane conservant les aires, Bull. Astron., 32 (1967), 267-285. | Zbl 0171.22902
[42] G. J. SUSSMAN - J. WISDOM, Numerical evidence that the motion of Pluto is chaotic, Science, 241 (1988), 433-437.

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali