On The Geometrical Description of Dynamical Stability

Details On The Geometrical Description of Dynamical Stability On The Geometrical Description of Dynamical Stability

2008-11-02

arxiv.org/abs/0811.0126v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

A general parametrization requirement for geometrization of dynamical stability is presented. We show that the non-physical behaviors appear in lower dimensional systems when non-affine parametrization of arc length with time is used. We compare the two widely used Jacobi and Eisenhart metrics as archetypes for (non)affine parametrization. We numerically investigate this in the context of the two-centered Morse potential. The relevance of parametric resonance as a source of instability in two dimensional systems is resolved.

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