On the existence of homoclinic and heteroclinic orbits for differential equations with a small parameter
1991 ◽
Vol 2
(2)
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pp. 133-158
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Keyword(s):
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.
2014 ◽
Vol 24
(08)
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pp. 1440003
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1988 ◽
Vol 109
(1-2)
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pp. 23-36
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2000 ◽
Vol 10
(12)
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pp. 2669-2687
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1994 ◽
Vol 109
(1)
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pp. 201-221
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2008 ◽
Vol 21
(1)
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pp. 45-71
1992 ◽
Vol 87
(5)
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pp. 1075-1086
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Keyword(s):
1924 ◽
Vol 22
(3)
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pp. 325-349
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