Fast instability indicator in few dimensional dynamical systems

Abstract

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. &#34;quickly&#34;) than the usual tools, like Lyapunov Characteristic Numbers (LCN&#39;s) or Poincare` Surface of Section. Moreover, at variance with other &#34;fast&#34; 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.