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Width of the homoclinic zone in the parameter space for quadratic maps
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Gelfreich, Vassili and Naudot, V. (2009) Width of the homoclinic zone in the parameter space for quadratic maps. Experimental Mathematics, Vol.18 (No.4). pp. 409-427. doi:10.1080/10586458.2009.10129058 ISSN 1058-6458.
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Official URL: http://dx.doi.org/10.1080/10586458.2009.10129058
Abstract
We study several families of planar quadratic diffeomorphisms near a Bogdanov-Takens bifurcation. For each family, the skeleton of the associated bifurcation diagram can be deduced from the interpolating flow. However, a zone of chaos confined between two lines of homoclinic bifurcation that are exponentially close to one another is observed. The goal of this paper is to test numerically an accurate asymptotic expansion for the width of this chaotic zone for different families.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Experimental Mathematics | ||||
| Publisher: | A K Peters, Ltd. | ||||
| ISSN: | 1058-6458 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.18 | ||||
| Number: | No.4 | ||||
| Number of Pages: | 19 | ||||
| Page Range: | pp. 409-427 | ||||
| DOI: | 10.1080/10586458.2009.10129058 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
| Grant number: | EP/COOO595/1 (EPSRC) |
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