A spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems

Regular and irregular motions of bounded conservative Hamiltonian systems of N degrees of freedom can be distinguished by the structure of the frequency spectrum of a single trajectory. The spectral entropy S is introduced which provides a measure of the distribution of the frequency components. Numerical calculations on the model Henon and Heiles system and a realistic molecular model are performed. Power spectra are obtained from numerical solutions to Hamilton's equations using fast Fourier transforms and the Hanning method. For regular trajectories S is found to stabilise after a finite time of integration, while for irregular cases S increases erratically. Estimates of the relative volume of regular regions of phase space as a function of energy are given for the two systems.