The nekhoroshev theorem and the asteroid belt dynamical system

Celestial Mechanics and Dynamical Astronomy

Volumn 65, Issue 1-2, 1996, Pages 107-136

  Morbidelli, Alessandro ^a   Guzzo, Massimiliano ^b  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Asteroids; Degenerate systems; Frequency analysis; Lyapunov exponents; Nekhoroshev theorem

Indexed keywords

EID: 26444577859     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf00048442     Document Type: Article

References (17)

1. Arnold, V., I.: 1963, Proof of A. N. Kolmogorov's theorem on the conservation of conditionally periodic motions with a small variation in the Hamiltonian., Russian Math. Surv., 18, No. 5, 9-36.
2. Benettin, G., Galgani L., and Giorgilli A.: 1985, A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems., Cel. Mech., 37, 1.
3. Benettin, G. and Gallavotti G.: 1986, Stability of motions near resonances in quasi-integrable Hamiltonian systems.. J. Stat. Phys., 44, 293-338.
4. Benettin, G., Fassò F. and Guzzo M.: 1996, Fast rotations of the rigid body: a study by Hamiltonian perturbation theory. Part II: gyroscopic rotations., preprint.
5. Bretagnon, P.: 1974, Termes à longues périodes dans le système solaire., Astron. Astrophys., 30, 141-154.
6. Chirikov, B. V.; 1979, A universal instability of many dimensional oscillator systems Physics reports, 52, 265-379.
7. Contopoulos, G.: 1967, in Nahon, F. and Hénon, M. (eds): Les nouvelles méthodes de la dynamique stellaire, CNRS, Paris (1966); see also Bull. Astron. Ser. 3, 2, Fasc. 1, 233.
8. see also Bull. Astron. Ser. 3, 2, Fasc. 1, 233.
9. Dermott, F. S. and Murray, C. D.: 1983, Nature of the Kirkwood gaps in the asteroid belt., Nature, 301, 201-205.
10. Farinella, P., Froeschlé, Ch. Froeschlé, C., Gonczi, R., Hahn, G., Morbidelli, A. and Valsecchi, G. B.: 1994, Asteroids falling onto the Sun, Nature, 371, 315-317.
11. Froeschlé C.: 1972, Numerical study of a four dimensional mapping, Astron. Astrophys., 16, 172-189.
12. Froeschlé C. and Lega E.: 1995, On the measure of the structure around the last KAM torus before and after its break-up, Celest. Mech., in press.
13. Giorgilli, A. and Morbidelli A.: 1996, Invariant KAM tori and global stability for Hamiltonian systems, ZAMP, in press.
14. Giorgilli, A. and Skokos C.: 1996, On the stability of the Trojan asteroids, Astron. Astrophys., in press.
15. Guzzo M. and Morbidelli A.; 1996, Construction of a Nekhoroshev like result for the asteroid belt dynamical system, Celest. Mech., submitted.
16. Laskar, J.,: 1990, The chaotic motion of the solar system: a numerical estimate of the size of the chaotic zones, Icarus, 88, 266-291.
17. Laskar J., Froeschlé C. and Celletti A: 1992, The measure of chaos by the numerical analysis of the fundamental frequencies. Application to the standard mapping, Physica D, 56, 253-269.