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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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:	Date Event May 2007 Published
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

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