Characterization of the Chaotic or Regular Nature of Dynamical Orbits: A New, Fast Method

A new method of characterization of the regular or chaotic nature of dynamical orbits has been discovered. It takes advantage of both morphological and dynamical properties of orbits, and can be applied to systems of all degrees of freedom. The new technique has been designed to analyze time-independent, time-dependent, and N-body systems. It can provide straightforward information about the transition of orbits from regular into chaotic and vice versa, which can happen in time-dependent regimes. Equally important is the distinction it can make between sticky and wildly chaotic epochs during the evolution of chaotic orbits in time-independent regimes. Its most important advantage over the existing methods is that, it characterizes an orbit using information from a very small number of orbital periods. For these reasons the new method is extremely promising to be useful and effective in a broad spectrum of disciplines.