Resonance bifurcation from homoclinic cycles |
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Authors: | Ramon Driesse |
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Institution: | KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, Netherlands |
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Abstract: | Differential equations that are equivariant under the action of a finite group can possess robust homoclinic cycles that can moreover be asymptotically stable. For differential equations in R4 there exists a classification of different robust homoclinic cycles for which moreover eigenvalue conditions for asymptotic stability are known. We study resonance bifurcations that destroy the asymptotic stability of robust ‘simple homoclinic cycles’ in four-dimensional differential equations. We establish that typically a periodic trajectory near the cycle is created, asymptotically stable in the supercritical case. |
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Keywords: | 34C37 37G40 |
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