Topological analysis for designing a suspension of the Henon map

Sylvain Mangiarotti (1) , Christophe Letellier (2)

1 CESBIO - Centre d'études spatiales de la biosphère
2 CORIA - Complexe de recherche interprofessionnel en aérothermochimie

A suspension of a map consists of the flow for which the Poincare section is that map. Designing a suspension of a given map remains a non-trivial task in general. The case of suspending the flenon map is here considered. Depending on the parameter values, the Henon map is orientation preserving or reversing; it is here shown that while a tridimensional suspension can be obtained in the former case, a four-dimensional flow is required to suspend the latter. A topological characterization of the three-dimensional suspension proposed by Starrett and Nicholas for the orientation preserving area is performed. A template is proposed for the four-dimensional case, for which the governing equations remain to be obtained. (C) 2015 Elsevier B.V. All rights reserved.

Domaines: Sciences de l'ingénieur [physics]

Sylvain Mangiarotti, Christophe Letellier. Topological analysis for designing a suspension of the Henon map. Physics Letters A, 2015, 379 (47-48), pp.3069--3074. ⟨10.1016/j.physleta.2015.10.016⟩. ⟨hal-01612369⟩