Computation of bifurcation manifolds of linearly independent homoclinic orbits |
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Authors: | Changrong Zhu Weinian Zhang |
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Institution: | a Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China b Department of Mathematics, Chongqing University, Chongqing 400044, PR China |
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Abstract: | Regarding the small perturbation as a parameter in an appropriate space of functions, we can discuss co-existence of homoclinic orbits for non-autonomous perturbations of an autonomous system in Rn and describe conditions of parameters for such degenerate homoclinic bifurcations with some bifurcation manifolds of infinite dimension. Since those manifolds determine the relation among parameters for such bifurcations, in this paper we give an algorithm to compute approximately those manifolds and concretely obtain their first order approximates. |
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Keywords: | 34C45 34C40 |
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