Probing the Nekhoroshev stability of asteroids

Celestial Mechanics and Dynamical Astronomy

Volumn 83, Issue 1-4, 2002, Pages 121-140

  Guzzo, Massimiliano ^a   Knežević, Zoran ^b   Milani, Andrea ^c  

^a UNIVERSITY OF PADOVA   (Italy)

^b Astronomska Opservatorija   (Serbia)

^c UNIVERSITY OF PISA   (Italy)

Author keywords

Asteroids; Long term stability; Nekhoroshev theorem

Indexed keywords

EID: 0141569434     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020182715182     Document Type: Article

References (40)

1. Benettin, G. and Fassò, F.: 1995, 'Fast rotations of the rigid body: a study by Hamiltonian perturbation theory. Part I', Nonlinearity 9, 137-186.
2. Benettin, G., Fassò, F. and Guzzo, M.: 1997, 'Fast rotations of the rigid body: a study by Hamiltonian perturbation theory. Part II: Gyroscopic Rotations', Nonlinearity 10, 1695-1717.
3. Benettin, G., Fassò, F. and Guzzo, M.: 1998, 'Nekhoroshev-stability of L4 and L5 in the spatial restricted three-body problem', Regular Chaot. Dyn. 3(3).
4. Benettin, G., Galgani, L. and Giorgilli, A.: 1985, 'A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems,' Celest. Mech. & Dyn. Astr 37(1).
5. Benettin, G. and Gallavotti, G.: 1986, 'Stability of motions near resonances in quasi-integrable Hamiltonian systems', J. Stat. Phys. 44, 293-338.
6. Bottke, W. F., Vokrouhlicý, D., Brož, M., Nesvorný, D. and Morbidelli, A.: 'Dynamical spreading of asteroid families via the Yarkovsky effect: the Koronis family and beyond', (preprint).
7. Carpino, M., Milani A. and Nobili, A. M.: 1987, 'Long term numerical integrations and synthetic theories for the motion of the outer planets', Astron. Astrophys. 181, 182-194.
8. Celletti, A. and Chierchia, L.: 1995, 'A constructive theory of Lagrangian tori and computer-assisted applications', Dynamics Reported, New Series, Springer Verlag 4.
9. Celletti, A. and Chierchia, L.: 1997, 'On the stability of realistic three-body problems', Comm. Math. Phys. 186(2), 413-449.
10. Celletti, A., Giorgilli, A. and Locatelli, U.: 2000, 'Improved estimates on the existence of invariant tori for Hamiltonian systems', Nonlinearity 13(2), 397-412.
11. Froeschlé, C., Lega, E. and Gonczi, R.: 1997, 'Fast Lyapunov indicators. Application to asteroidal motion', Celest. Mech. & Dyn. Astr. 67, 41-62.
12. Froeschlé, C., Guzzo, M. and Lega, E.: 2000, 'Graphical evolution of the Arnold web: from order to chaos', Science 289(5487).
13. Guzzo M.: 1999, 'Nekhoroshev stability of quasi-integrable degenerate Hamiltonian systems', Regular Chaot. Dyn. 4(2).
14. Guzzo, M.: 2001, (preprint).
15. Guzzo, M. and Benettin, G.: 2001, 'A spectral formulation of the Nekhoroshev theorem and its relevance for numerical and experimental data analysis', Discrete Cont. Dyn. Sys. Series B 1(1).
16. Guzzo, M., Lega, E. and Froeschlé, C.: 2001, 'On the numerical detection of the effective stability of chaotic motions in quasi-integrable systems', Physica D (accepted).
17. Guzzo, M. and Morbidelli, A.: 1997, 'Construction of a Nekhoroshev like result for the asteroid belt dynamical system', Celest. Mech. & Dyn. Astr. 66, 255-292.
18. Knežević, Z. and Jovanović, B.: 1997, 'Is the chaotic clock ticking correctly?', Bull. Astr. Belgrade 156, 4769.
19. Knežević Z. and A. Milani 1999, 'Higher order and iterative theories to compute asteroid mean elements', In: J. Henrard and S. Ferraz-Mello (eds), Impact of Modern Dynamics in Astronomy, Kluwer Academic Publisher, pp. 359-360.
20. Knežević, Z. and Milani, A.: 2000, 'Synthetic proper elements for outer main belt asteroids', Celest. Mech. & Dyn. Astr. 78, 17-46.
21. 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.
22. Laskar, J.: 1990, 'The chaotic motion of the solar system. A numerical estimate of the size of the chaotic zones', Icarus 88, 266-291.
23. Lega, E. and Froeschlé, C.: 1997, 'Fast Lyapunov indicators. Comparison with other chaos indicators. Application to two and four dimensional maps', In: J. Henrard and R. Dvorak (eds), Dynamical Behavior of our Planetary System, Kluwer Academic Publisher.
24. Locatelli, U. and Giorgilli, A.: 2000, 'Invariant tori in the secular motions of the three-body planetary systems', Celest. Mech. & Dyn. Astr. 78, 47-74.
25. Lochak, P.: 1992, 'Canonical perturbation theory via simultaneous approximation', Russ. Math. Surv. 47, 57-133.
26. Milani, A.: 1995, 'Proper elements and stable chaos', In: A. E. Roy and and B. A. (eds), From Newton to Chaos, Plenum Press, pp. 47-78.
27. Milani, A. and Farinella, P.: 1994, 'The age of the Veritas asteroid family deduced by chaotic chronology', Nature 370, 40-42.
28. Milani, A. and Nobili, A. M.: 1988, 'Integration error over very long time spans', Celest. Mech. & Dyn. Astr. 43, 1-34.
29. Milani, A. and Knežević, Z.: 1992, 'Asteroid proper elements and secular resonances', Icarus, 98, 211-232.
30. Milani, A. and Knežević, Z.: 1994, 'Asteroid proper elements and the dynamical structure of the asteroid main belt,' Icarus 107, 219-254.
31. Milani, A., Nobili, A. and Knežević, Z.: 1997, 'Stable chaos in the asteroid belt', Icarus 125, 13-31.
32. Morbidelli, A. and Guzzo, M.: 1997, 'The Nekhoroshev theorem and the asteroid belt dynamical system', Celest. Mech. & Dyn. Astr. 65, 107-136.
33. Morbidelli, A. and Nesvorny, D.: 1999, 'Numerous weak resonances drive asteroids toward terrestrial planets orbits', Icarus 139, 295-308.
34. Nekhoroshev, N. N.: 1977, 'Exponential estimates of the stability time of near-integrable Hamiltonian systems', Russ. Math. Surv. 32, 1-65.
35. Nekhoroshev, N. N., 1979, 'Exponential estimates of the stability time of near-integrable Hamiltonian systems', 2 Trudy Sem. Petrovs. 5, 5-50.
36. Nesvorny, D. and Morbidelli A.: 1998, 'Three-body mean motion resonances and the chaotic structure of the asteroid belt', Astr. J. 116, 3029-3037.
37. Niederman, L.: 1996, 'Stability over exponentially long times in the planetary problem', Nonlinearity 9, 1703-1751.
38. Niederman, L.: 2000, 'Exponential stability for small perturbations of steep integrable Hamiltonian systems', (preprint).
39. Pöschel, J.: 1993, 'Nekhoroshev's estimates for quasi-convex Hamiltonian systems', Math. Z. 213, 187.
40. Robutel, P. and Laskar, J.: 2000, 'Frequency map and global dynamics in planetary systems short period dynamics of massless particle', In: Planetary Systems in the Universe, International Astronomical Union. Symposium No. 202. Manchester, England, August 2000.