Universality in Three-Frequency Resonances

Details Universality in Three-Frequency Resonances Universality in Three-Frequency Resonances

1999-05-20

arxiv.org/abs/chao-dyn/9905034v1

Phys. Rev. E 59, 2902-2906, 1999

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevE.59.2902

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.

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