ar X iv : n lin / 0 10 80 08 v 1 [ nl in . C D ] 7 A ug 2 00 1 FAST INSTABILITY INDICATOR IN FEW DIMENSIONAL DYNAMICAL SYSTEMS

Using the tools of Differential Geometry, we define a new fast chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e., quickly) than the usual tools, like Lyapunov Characteristic Numbers (LCN’s) or Poincaré Surface of Section. Moreover, at variance with other fast indicators proposed in the Literature, it gives informations about the asymptotic behaviour of trajectories, though being local in phase-space. Furthermore, it detects the chaotic or regular nature of geodesics without any reference to a given perturbation and it allows also to discriminate between different regimes (and possibly sources) of chaos in distinct regions of phase-space.