2003/03/31 by Radha Balakrishnan, Balakrishnan, Radha, Indubala I. Satija +2
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0303071
arxiv created 2003/03/31 · openalex publication_date 2003/03/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.