Abstract
Frequency analysis is a new method for analyzing the stability of orbits in a conservative dynamical system. It was first devised in order to study the stability of the solar system (Laskar, Icarus, 88, 1990). It is a powerful method for analyzing weakly chaotic motion in hamiltonian systems or symplectic maps. For regular motions, it yields an analytical representation of the solutions. In cases of 2 degrees of freedom system with monotonous torsion, precise numerical criterions for the destruction of KAM tori can be found. For a 4D symplectic map, plotting the frequency map in the frequency plane provides a clear representation of the global dynamics and describes the actual Arnold web of the system.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Froeschlé, C.: 1972, ‘Numerical study of a four-dimensional mapping’,Astron. Astrophys.,16, 172–189
Greene, J.M.: 1979, ‘A method for determining stochastic transitions’,J. Math. Phys.,20, 1183
Laskar, J.: 1990, ‘The chaotic behaviour of the solar system: A numerical estimate of the size of the chaotic zones’,Icarus,88, 266–291
Laskar, J.: 1992, ‘Frequency analysis of multidimensional systems. Global dynamics and diffusion’,submitted to Physica D
Laskar, J., Froeschlé, C., 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
Pöschel, J.: 1982,Commun. Pure. Appl. Math.,35 653
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Laskar, J. Frequency analysis of a dynamical system. Celestial Mech Dyn Astr 56, 191–196 (1993). https://doi.org/10.1007/BF00699731
Issue Date:
DOI: https://doi.org/10.1007/BF00699731