Frequency analysis of a dynamical system
Frequency analysis method was devised to study stability of motions in the solar system and was proved to be a powerful method for analyzing the stability of orbits in a conservative dynamical system, particularly, weakly chaotic motions in Hamiltonian systems or symplectic maps. For regular motion it yields an analytical representation of the solutions. In this paper the author shows precise numerical criteria for the destruction of KAM tori for the case of dynamical systems of two degrees of freedom with monotonous torsion. It is also shown that 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.
scientific article; zbMATH DE number 429321