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Zbl 0932.37032
Zhu, Deming
Problems in homoclinic bifurcation with higher dimensions. (English)
[J] Acta Math. Sin., New Ser. 14, No.3, 341-352 (1998). ISSN 1000-9574; ISSN 1439-7617/e

Summary: A suitable local coordinate system is constructed by using exponential dichotomies and generalizing the Floquet method from periodic systems to nonperiodic systems. Then the Poincaré map is established to solve various problems in homoclinic bifurcation with codimension one or two. Bifurcation diagrams and bifurcation curves are given.
MSC 2000:
*37G15 Bifurcations of limit cycles and periodic orbits
37G25 Bifurcations connected with nontransversal intersection

Keywords: exponential dichotomy; local coordinates; homoclinic bifurcation; periodic orbit

Cited in: Zbl 1257.34026 Zbl 1242.34081 Zbl 1165.34358

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