Resonances for weak coupling of the unfolding of a saddle-node periodic orbit with an oscillator
Baesens, C. and MacKay, R. S. (Robert Sinclair). (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. ISSN 0951-7715Full text not available from this repository.
Official URL: http://dx.doi.org/10.1088/0951-7715/20/5/012
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.|
|Official Date:||May 2007|
|Number of Pages:||16|
|Page Range:||pp. 1283-1298|
|Access rights to Published version:||Restricted or Subscription Access|
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