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Resonance regions for families of torus maps

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Kim, Seunghwan, MacKay, Robert S. and Guckenheimer, J. (1989) Resonance regions for families of torus maps. NONLINEARITY, 2 (3). pp. 391-404. doi:10.1088/0951-7715/2/3/001

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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, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: NONLINEARITY
Publisher: IOP PUBLISHING LTD
ISSN: 0951-7715
Official Date: August 1989
Dates:
DateEvent
August 1989UNSPECIFIED
Volume: 2
Number: 3
Number of Pages: 14
Page Range: pp. 391-404
DOI: 10.1088/0951-7715/2/3/001
Publication Status: Published

Data sourced from Thomson Reuters' Web of Knowledge

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