Email this article 
Lyapunov exponents in fundamental models of nonlinear resonance
- Authors: Shevchenko I.I1
-
Affiliations:
- Issue: Vol 120, No 7-8 (2024)
- Pages: 650-650
- Section: Articles
- URL: https://journals.rcsi.science/0370-274X/article/view/267724
- DOI: https://doi.org/10.31857/S0370274X24100249
- EDN: https://elibrary.ru/WHMFYK
- ID: 267724
Cite item
Open Access
Access granted
Subscription Access
Abstract
The problem of analytical estimation of the Lyapunov exponents and Lyapunov timescales of the motion in multiplets of interacting nonlinear resonances is considered. To this end, we elaborate a unified framework, based on the separatrix map theory, which incorporates both an earlier approach for the first fundamental model of perturbed resonance (given by the perturbed pendulum Hamiltonian) and a new one for its second fundamental model (given by the perturbed Andoyer Hamiltonian). Within this framework, new accurate estimates for the Lyapunov timescales of the inner and outer subsystems of the Solar planetary system are presented and discussed.
References
- B. V. Chirikov, Phys. Rep. 52, 263 (1979).
- A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, Springer, N.Y. (1992).
- J. D. Meiss, Rev. Modern Phys. 64, 795 (1992).
- J. Henrard and A. Lemaˆıtre, Celest. Mech. 30, 197 (1983).
- I. I. Shevchenko, Dynamical Chaos in Planetary Systems, Springer Nature, Cham (2020).
- I. I. Shevchenko, Cosmic Res. 40, 296 (2002).
- I. I. Shevchenko, Phys. Lett. A 378, 34 (2014).
- I. I. Shevchenko, On the Lyapunov exponents of the asteroidal motion subject to resonances and encounters, ed. by A. Milani, G. B. Valsecchi, and D. Vokrouhlicky´, Near Earth Objects, our Celestial Neighbors: Opportunity and Risk (Proceedings IAU Symposium 236), Cambridge University Press, Cambridge (2007), p. 15.
- K. Batygin, A. Morbidelli, and M. J. Holman, Astrophys. J. 799, 120 (2015).
- N. Murray and M. Holman, Science 283, 1877 (1999).
Supplementary files
