Kim, Seunghwan, MacKay, R. S. 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

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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
Date:	August 1989
Volume:	2
Number:	3
Number of Pages:	14
Page Range:	pp. 391-404
Identification Number:	10.1088/0951-7715/2/3/001
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/24055

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