  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 Poincare` 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.
