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Determining the number of integrals of motion by an adapted correlation dimension method
1Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
Abstract:
An adapted correlation dimension algorithm is used to numerically determine the number of integrals of motion in a variety of conservative classical systems. The method is demonstrated on three sample systems that display various degrees of integrable and chaotic behavior: the Hénon-Heiles Hamiltonian, an asymmetric top molecule in an electric field, and the planetary system HD128311. Two additional applications of the method emerge: using the adapted correlation dimension algorithm (a) to study partial barriers and turnstiles in phase space and (b) to predict the long-time stability of planetary systems using short-time data.
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