A fast method for distinguishing between ordered and chaotic orbits

Wedescribe a newmethod of distinguishing between ordered and chaotic orbits, which is much faster than the methods used up to now, namely (1) the distribution of the Poincaré consequents, (2) the Lyapunov characteristic number and (3) the distribution of the rotation angles. This method is based on the distribution of the helicity angles (the angles of small deviations ξ 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 successive deviations | ξ |, also called ’short time Lyapunov characteristic numbers’). We apply this method to 2-D mappings and 4-D mappings, representing Hamiltonian systems of 2 and 3 degrees of freedom respectively.