METHOD FOR DISTINGUISHING BETWEEN ORDERED AND CHAOTIC ORBITS IN 4-DIMENSIONAL MAPS

The usual methods for distinguishing ordered and chaotic orbits in thr ee-dimensional (3D) Hamiltonian systems, or 4D maps, are either ineffi cient (because we cannot visualize 4D figures), or slow (e.g., the cal culation of Lyapunov characteristic numbers). Here we provide an effic ient and fast method, based on the spectra of stretching numbers (shea -time Lyapunov characteristic numbers), or helicity angles (angles of infinitesimal deviations from an orbit with a fixed direction). The sp ectra for two different initial deviations are the same for chaotic or bits, but different for ordered orbits. We apply this method to a diff icult case of weak chaos (small Lyapunov characteristic number), and p rove its advantages with respect to other methods. Finally we explain the different behavior of ordered and chaotic orbits theoretically.