Fast instability indicator in few dimensional dynamical systems

Piero Cipriani; Maria Teresa Di Bari

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arXiv · nlin/0108008

Fast instability indicator in few dimensional dynamical systems

Piero Cipriani·Maria Teresa Di Bari

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Abstract

Using the tools of Differential Geometry, we define a new < > 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.

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nlin.CD astro-ph cond-mat.stat-mech math-ph math.MP physics.comp-ph

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Piero Cipriani, Maria Teresa Di Bari. 2001-08-07. Fast instability indicator in few dimensional dynamical systems. https://arxiv.org/abs/nlin/0108008

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