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 informationentropy 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 classi.ed 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)