Width of the homoclinic zone in the parameter space for quadratic maps
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. ISSN 1058-6458Full text not available from this repository.
Official URL: http://dx.doi.org/10.1080/10586458.2009.10129058
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 > Mathematics|
|Journal or Publication Title:||Experimental Mathematics|
|Publisher:||A K Peters, Ltd.|
|Number of Pages:||19|
|Page Range:||pp. 409-427|
|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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