Frequency analysis of a dynamical system

Details Frequency analysis of a dynamical system Frequency analysis of a dynamical system

May 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..56..191l&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 56, no. 1-2, p. 191-196.

Computer Science

Numerical Analysis

47

Chaos, Dynamical Systems, Frequency Analyzers, Numerical Analysis, Solar System, Systems Stability, Degrees Of Freedom, Hamiltonian Functions

Scientific paper

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. 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 two-DOF system with monotonic torsion, precise numerical criteria 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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