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Bifurcations of heteroclinic loops. (English) Zbl 0993.34040
Summary: By generalizing the Floquet method from periodic systems to systems with exponential dichotomy, a local coordinate system is established in a neighborhood of a heteroclinic loop Γ to study the bifurcation problems of homoclinic and periodic orbits. Asymptotic expressions for the bifurcation surfaces and their relative positions are given. Results obtained in the literature concerning 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 noncoexistence of 1-hom and 1-per orbits and nonexistence of 2-hom and 2-per orbits are also obtained.

34C23Bifurcation (ODE)
34C37Homoclinic and heteroclinic solutions of ODE
34C25Periodic solutions of ODE
34C28Complex behavior, chaotic systems (ODE)
34D09Dichotomy, trichotomy
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