Fast Instability Indicator in Few Dimensional Dynamical Systems

Details Fast Instability Indicator in Few Dimensional Dynamical Systems Fast Instability Indicator in Few Dimensional Dynamical Systems

Dec 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002nmgm.meet..897c&link_type=abstract

"THE NINTH MARCEL GROSSMANN MEETING On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and R

Physics

Scientific paper

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 geodesies 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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