The Library
Resonances for weak coupling of the unfolding of a saddle-node periodic orbit with an oscillator
Tools
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 ISSN 0951-7715.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1088/0951-7715/20/5/012
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, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Nonlinearity | ||||
Publisher: | Institute of Physics Publishing Ltd. | ||||
ISSN: | 0951-7715 | ||||
Official Date: | May 2007 | ||||
Dates: |
|
||||
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
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |