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Open Access item Universality in three-frequency resonances

Authors:Cartwright, Julyan H. E.
González, Diego L.
Piro, Oreste
Issue Date:1999
Publisher:American Physical Society
Citation:Physical Review E- Statistical, Nonlinear, and Soft Matter Physics E 59: 2902–2906 (1999)
Abstract:We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothesize an ordering of these resonances based on a generalization of the Farey tree organization from two frequencies to three. In experiments and numerical simulations we demonstrate that our hypothesis describes the hierarchies of three-frequency resonances in representative dynamical systems. We conjecture that this organization may be universal across a large class of three-frequency systems.
Description:PACS numbers: 05.45.2a
Publisher version (URL):http://dx.doi.org/10.1103/PhysRevE.59.2902
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