Universality in Three-Frequency Resonances
chao-dyn
2012-07-30 v1 Dynamical Systems
Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.chao-dyn/9905034,
title = {Universality in Three-Frequency Resonances},
author = {Julyan H. E. Cartwright and Diego L. Gonzalez and Oreste Piro},
journal= {arXiv preprint arXiv:chao-dyn/9905034},
year = {2012}
}