Universality in three-frequency resonances

We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothes ize an ordering of these resonances based on a generalization of the Farey tree organization from two frequencies to three. In experiments and numeric al simulations we demonstrate that our hypothesis describes the hierarchies of three-frequency resonances in representative dynamical systems. We conj ecture that this organization may be universal across a large class of thre e-frequency systems. [S1063-651X(99)14803-7].