Bifurcations of heteroclinic loops |
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Authors: | Deming Zhu Zhihong Xia |
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Institution: | (1) Department of Mathematics, East China Normal University, 200062 Shanghai, China;(2) Department of Mathematics, Northwestern University, 60208 Evanston, IL, USA |
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Abstract: | By generalizing the Floquet method from periodic systems to systems with exponential dichotomy, a local coordinate system
is established in a neighborhood of the heteroclinic loop Γ to study the bifurcation problems of homoclinic and periodic orbits.
Asymptotic expressions of the bifurcation surfaces and their relative positions are given. The results obtained in literature
concerned with the 1-hom bifurcation surfaces are improved and extended to the nontransversal case. Existence regions of the
1-per orbits bifurcated from Γ are described, and the uniqueness and incoexistence of the 1-hom and 1-per orbit and the inexistence
of the 2-hom and 2-per orbit are also obtained.
Project supported by the National Natural Science Foundation of China (Grant No. 19771037) and the National Science Foundation
of America # 9357622. This paper was completed when the first author was visiting Northwestern University. |
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Keywords: | heteroclinic orbit homoclinlc bifurcation periodic orbit bifurcation |
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