Anholonomy and Geometrical Localization in Dynamical Systems

Details Anholonomy and Geometrical Localization in Dynamical Systems Anholonomy and Geometrical Localization in Dynamical Systems

2003-03-31

arxiv.org/abs/nlin/0303071v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

We characterize the geometrical and topological aspects of a dynamical system by associating a geometric phase with a phase space trajectory. Using the example of a nonlinear driven damped oscillator, we show that this phase is resilient to fluctuations, responds to all bifurcations in the system, and also finds new geometric transitions. Enriching the phase space description is a novel phenomenon of ``geometrical localization'' which manifests itself as a significant deviation from planar dynamics over a short time interval.

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