Abstract
We propose a criterion for the destruction of a two-dimensional torus through the formation of an infinite set of cusp points on the closed invariant curves defining the resonance torus. This mechanism is specific to noninvertible maps. The cusp points arise when the tangent to the torus at the point of intersection with the critical curve coincides with the eigendirection corresponding to vanishing eigenvalue for the noninvertible map. Further parameter changes lead typically to the generation of loops (self-intersections of the invariant manifolds) followed by the transformation of the torus into a complex chaotic set.
- Received 13 November 2002
DOI:https://doi.org/10.1103/PhysRevE.67.046215
©2003 American Physical Society