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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 ${\Gamma }$ 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 ${\Gamma }$ 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.

##### MSC:
 34C23 Bifurcation (ODE) 34C37 Homoclinic and heteroclinic solutions of ODE 34C25 Periodic solutions of ODE 34C28 Complex behavior, chaotic systems (ODE) 34D09 Dichotomy, trichotomy
##### References:
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