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- Title
On the existence of homoclinic and heteroclinic orbits for differential equations with a small parameter.
- Authors
Byatt-Smith, John G.
- Abstract
Low order differential equations typically have solutions which represent homoclinic or heteroclinic orbits between singular points in the phase plane. These orbits occur when the stable manifold of one singular point intersects or coincides with its unstable manifold, or the unstable manifold of another singular point. This paper investigates the persistence of these orbits when small dispersion is added to the system. In the perturbed system the stable manifold of a singular point passes through an exponentially small neighbourhood of a singular point and careful analysis is required to determine whether a homoclinic or heteroclinic connection is achieved.
- Publication
European Journal of Applied Mathematics, 1991, Vol 2, Issue 2, p133
- ISSN
0956-7925
- Publication type
Article
- DOI
10.1017/S0956792500000449