Variational computation of homoclinic orbits for twist maps

Variational methods have been used extensively in the study and computation of monotone twist maps of the annulus (dimension d = 1), and in their higher dimensional generalizations. In particular, periodic orbits can be characterized and computed as critical points of certain real-valued functions,...

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Bibliographic Details
Published in:Physica. D 1995-08, Vol.85 (4), p.548-562
Main Author: Tabacman, Eduardo
Format: Article
Language:English
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Summary:Variational methods have been used extensively in the study and computation of monotone twist maps of the annulus (dimension d = 1), and in their higher dimensional generalizations. In particular, periodic orbits can be characterized and computed as critical points of certain real-valued functions, constructed from the generating function of the map. In this paper we propose a similar variational method for the computation of orbits homoclinic (or heteroclinic in some cases) to periodic orbits. This again consists in finding critical points of a certain function, constructed with knowledge of the generating function of the map and of the stable and unstable manifolds to the periodic orbits near the periodic points. We also prove that under relatively simple conditions, when d = 1, there exist heteroclinic connections between fixed points.
ISSN:0167-2789
1872-8022
DOI:10.1016/0167-2789(95)00043-4