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Resonances for weak coupling of the unfolding of a saddle-node periodic orbit with an oscillator

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Baesens, C. and MacKay, Robert S. (2007) Resonances for weak coupling of the unfolding of a saddle-node periodic orbit with an oscillator. Nonlinearity, Vol.20 (No.5). pp. 1283-1298. doi:10.1088/0951-7715/20/5/012

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Official URL: http://dx.doi.org/10.1088/0951-7715/20/5/012

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Abstract

For a family of continuous-time dynamical systems with two angle variables, a resonance is a set of parameter values such that some integer combination of the ( lifted) angles remains bounded for some orbits. For weak coupling of an unfolding of a saddle-node periodic orbit with an oscillator, it is shown that the low order resonances have at least a certain amount of bifurcation structure. Furthermore, define a Chenciner bubble to be the complement of the set of parameters near a resonance for which there is an attractor-repellor pair consisting of two C-1 invariant tori, or a C-1 invariant torus attracting from one side and repelling from the other, or locally empty non-wandering set. The low order Chenciner bubbles are shown to have at least a certain structure. Chenciner's results for resonances in the unfolding of a degenerate Neimark-Sacker bifurcation can be seen as a special case of ours.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Nonlinearity
Publisher: Institute of Physics Publishing Ltd.
ISSN: 0951-7715
Official Date: May 2007
Dates:
DateEvent
May 2007Published
Volume: Vol.20
Number: No.5
Number of Pages: 16
Page Range: pp. 1283-1298
DOI: 10.1088/0951-7715/20/5/012
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

Data sourced from Thomson Reuters' Web of Knowledge

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