THE FAST LYAPUNOV INDICATOR - A SIMPLE TOOL TO DETECT WEAK CHAOS - APPLICATION TO THE STRUCTURE OF THE MAIN ASTEROIDAL BELT

A new method is presented, based on the variation with time of the len gth of vectors evolving in-tangential space, which distinguishes very quickly between regular and chaotic motion. This method is closely rel ated to the computation of the Lyapunov characteristic exponents, but because of the speed of computation it can be easily applied to the st udy of a large set of orbits. This method is tested for the 2-dimensio nal standard mapping, and the structure of the phase space is explored for the 4-dimensional standard map simulating the conditions of the d istribution of asteroids. Then the distribution of the 716 asteroids o rbiting between the 3/1 and 5/2 Kirkwood gaps is studied. (C) 1997 Els evier Science Ltd.