Abstract
In this paper, we study the bifurcation problems of rough heteroclinic loops connecting three saddle points for a higher-dimensional system. Under some transversal conditions and the nontwisted condition, the existence, uniqueness, and incoexistence of the 1-heteroclinic loop with three or two saddle points, 1-homoclinic orbit and 1-periodic orbit near Γ are obtained. Meanwhile, the bifurcation surfaces and existence regions are also given. Moreover, the above bifurcation results are extended to the case for heteroclinic loop with l saddle points.
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Project supported by the National Natural Science Foundation of China (10071022), and Shanghai Municipal Foundation of Selected Academic Research.
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Jin, Y.L., Zhu, D.M. Bifurcations of Rough Heteroclinic Loops with Three Saddle Points. Acta Math Sinica 18, 199–208 (2002). https://doi.org/10.1007/s101140100139
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DOI: https://doi.org/10.1007/s101140100139