A FAST METHOD FOR DISTINGUISHING BETWEEN ORDERED AND CHAOTIC ORBITS

We describe a new method of distinguishing between ordered and chaotic orbits, which is much faster than the methods used up to now, namely (1) the distribution of the Poincare consequents, (2) the Lyapunov cha racteristic number and (3) the distribution of the rotation angles. Th is method is based on the distribution of the helicity angles (the ang les of small deviations xi from a given orbit with a fixed direction), or of the twist angles (the differences of successive helicity angles ), and the stretching numbers (the logarithms of the ratios of success ive deviations \xi\, also called 'short time Lyapunov characteristic n umbers'). We apply this method to 2-D mappings and 4-D mappings, repre senting Hamiltonian systems of 2 and 3 degrees of freedom respectively .