Bifurcations of heteroclinic loops
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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.
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- Bifurcations of heteroclinic loops
Science in China Series A: Mathematics
Volume 41, Issue 8 , pp 837-848
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- heteroclinic orbit
- homoclinlc bifurcation
- periodic orbit bifurcation