Frequency analysis of a dynamical system |
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| Authors: | Jacques Laskar |
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| Institution: | (1) Bureau des Longitudes, Equipe Astronomie et Systèmes Dynamiques, 77 Avenue Denfert-Rochereau, F75014 Paris, France |
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| 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. |
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| Keywords: | Frequency analysis chaotic motion symplectic maps |
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