Fast Lyapunov indicators. Application to asteroidal motion

Celestial Mechanics and Dynamical Astronomy

Volumn 67, Issue 1, 1997, Pages 41-62

  Froeschlé, Claude ^a   Lega, Elena ^a,b   Gonczi, Robert ^a  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b CNRS LATAPSES   (France)

Author keywords

Detection of chaotic motion; Dynamical systems; Lyapunov exponents

Indexed keywords

EID: 0002443585     PISSN: 09232958     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008276418601     Document Type: Article

References (28)

1. Benettin, G., Galgani, L. and Strelcyn, J. M.: 1976, Phys. Rev. A, 14, 2338.
2. Benettin, G. and Galgani, L.: 1979, Lyapunov characteristic exponents and Stochasticity, Intrinsic Stochasticity in plasmas. Laval G. and Gresillon, D. (eds), Les éditions de Physique Coutaboeuf Orsay-France.
3. Benettin, G., Galgani, L., Giorgilli, A. and Strelcyn, J. M.: 1980, Lyapunov characteristic exponents for smooth dynamical systems; a method for computing all of them. Meccanica, 15: Part I : theory, 9-20 - Part II: Numerical applications, 21-30.
4. Celletti, A. and Froeschlé, C.: 1995, On the determination of the stochasticity threshold of invariant curves. Int. J. of Bifurcation and Chaos, 5, n.6.
5. Contopoulos, G., Galgani, L. and Giorgilli, A.: 1978, Rhys. Rev. A., 18, 1183.
6. Contopoulos, G., Voglis, N., Efthymiopoulos, C., Froeschlé, C., Gonczi, R., Lega, E., Dvorak, R. and Lohinger, E.: 1996, Transition spectra of dynamical systems. Celest. Mech. and Dynamical Astron., submitted.
7. Contopoulos, G. and Voglis, N.: 1996a, A fast method for distinguishing between ordered and chaotic motion. Astron. Astrophys., in press.
8. Franklin, F.: 1994, AJ, 107: 1890.
9. Froeschlé, C.: 1970, A numerical study of the stochasticity of dynamical systems with two degrees of freedom. Astron. and Astrophys., 9:15-23.
10. Froeschlé, C. and Gonczi, R.: 1980, Lyapunov characteristic numbers and Kolmogorov entropy of a four-dimensional mapping. Il Nouvo Cimento, 55B: 59-69.
11. Froeschlé, C.: 1984, The Lyapunov characteristic exponents and applications. Journal de Méc. théor. et apll., Numero spécial: 101-132.
12. Froeschlé, C., Froeschlé, Ch. and Lohinger, E.: 1993, Generalized Lyapunov characteristic indicators and corresponding Kolmogorov like entropy of the standard mapping. Celest. Mech. and Dynamical Astron., 56: 307-315.
13. Froeschlé, C. and Lega, E.: 1996, On the measure of the structure around the last KAM torus before and after its break-up. Celest. Mech. and Dynamical Astron., 64: 21-31.
14. Froeschlé, C. and Scheidecker, J. P.: 1973, Numerical study of a four dimensional mapping II. Astron. Astrophys., 22: 431-436.
15. Froeschlé, C. and Scheidecker, J. P.: 1973, On the disappearance of isolating integrals in systems with more than two degrees of freedom. Astrophys. and Space Sc., 25: 373-386.
16. Henon, M.: 1981, Cours des Houches XXXVI. North Holland, Amsterdam 57.
17. Hénon, M. and Heiles, C.: 1964, The applicability of the third integral of motion: Some numerical experiments. A. J., 1:73-79.
18. 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.
19. Lecar, M., Franklin, F. and Murison, M.: 1992, AJ, 104: 1230.
20. Lyapunov, A. M.: 1949, Problème General de la Stabilité du Muvement. Ann. Math. Studies. Princeton University Press., 17.
21. Milani, A., Nobili, A. and Knezevic, Z.: 1995, Icarus, submitted.
22. Milani, A. and Groupe E.U.R.O.P.A.: 1996, Celest.Mech. and Dynam. Astr., The Trojan asteroid belt: proper elements, stability, chaos and families. Celest. Mech. and Dynam. Astr., 57: 59-94.
23. Milani, A. and Nobili, A.: 1992, An example of stable chaos in the Solar System. Nature, 357: 569-571.
24. Morbidelli, A. and Froeschlé. C.: 1996, On the relationship between Lyapunov times and macroscopic instability times. Celest. Mech. and Dynam. Astr., 63: 227-239.
25. Murison, M., Lecar, M. and Franklin, F.: 1994, Chaotic motion in the outer asteroid belt and its relation to the age of the Solar System. AJ, 108: 2323-2329.
26. Oseledec, V. I.: 1968, A multiplicative ergodic theorem. The Lyapunov characteristic numbers of dynamical systems. Mosc. Math. Soc., 19: 197-231.
27. Soper, M., Franklin, F. and Lecar, M.: 1990, On the original distribution of the asteroids. Icarus, 87: 265-284.
28. Voglis, N. and Contopoulos, G. J.: 1994, J. Phys. A: Math. Gen., 27: 4899-4909.