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Resonance regions for families of torus maps

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Kim, Seunghwan, MacKay, R. S. (Robert Sinclair) and Guckenheimer, J.. (1989) Resonance regions for families of torus maps. NONLINEARITY, 2 (3). pp. 391-404. ISSN 0951-7715

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Abstract

A resonance region for a family of torus maps f: T-n -> T-n is the set of parameter values for which there exists a periodic orbit with a given rotation vector. For generic periodic families, resonance regions are projections of multiply connected manifolds. In many cases these are tori. Numerical studies of the case n = 2 illustrate the complicated internal bifurcation structure of the resonance regions. Codimension-two bifurcations and transversal homoclinic orbits are shown to exist. We discuss the significance of our findings for the transition to chaos from three-frequency quasiperiodic

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics
Q Science > QC Physics

Divisions:

Faculty of Science > Mathematics

Journal or Publication Title:

NONLINEARITY

Publisher:

IOP PUBLISHING LTD

ISSN:

0951-7715