Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems
We consider a singularly perturbed system depending on two parameters with two (possibly the same) normally hyperbolic centre manifolds. We assume that the unperturbed system has an orbit connecting a hyperbolic fixed point on one centre manifold to a hyperbolic fixed point on the other. Then we p...
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| Date: | 2008 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2008
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| Series: | Український математичний журнал |
| Subjects: | |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems / F. Battelli, K.J. Palmer // Український математичний журнал. — 2008. — Т. 60, № 1. — С. 28–55. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We consider a singularly perturbed system depending on two parameters with two (possibly the same)
normally hyperbolic centre manifolds. We assume that the unperturbed system has an orbit connecting a
hyperbolic fixed point on one centre manifold to a hyperbolic fixed point on the other. Then we prove
some old and new results concerning the persistence of these connecting orbits and apply the results to find
examples of systems in dimensions greater than three which possess Sil’nikov saddle-focus homoclinic
orbits. |
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