Orbital complexity in a time-dependent potential

We introduce a method to detect irregular or chaotic orbits in gravitational potentials based on a wavelet transform of stellar orbits. The method is based on a treatment of normalised frequency power-spectrum coefficients, which we interpret as occupation probabilities (or, weights) of individual frequency modes. Each probability is fed to a Shannon information-entropy formula, before summing over the whole spectrum to compute the total entropy S. This entropy is then monitored in time as the wavelet coefficients change: each orbit is classified as regular or not according to S and its dispersion. We find that diagrams of entropy versus entropy dispersion allow to identify orbits in a simple and efficient way, similarly to surface-of-section analysis but requiring less integration time. We apply the method to the case of a gravitational potential modulated by the periodic motion of a massive black hole and find that some 19% of stars are now shifted to highly irregular motion as a result of black hole orbital motion. This is the same fraction of stars that orbit within the black hole radius of influence. (C) 2008 WILEY-VCH Verlag GmbH&Co. KGaA,Weinheim