Homoclinic loop bifurcations on a Möbius band

Louis-Sébastien Guimond

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Homoclinic loop bifurcations on a Möbius band

机译：Homoclinic loop bifurcations on a Möbius band

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In this paper, we study 1-homoclinic loop bifurcations on a non-orientable 2-manifold: the Möbius band. The techniques for studying bifurcating dynamics of the 1-homoclinic loop on this manifold are similar to those for a figure-eight loop in the plane. We adapt the techniques revealed in a paper by Jebrane and Mourtada (1994 Cyclicité finie des lacets doubles non triviaux71349-65) covering the subject: we are able, studying the 2-return map where it exists, to give an explicit bound for the cyclicity of the 1-homoclinic loop for all arbitrary finite codimensions. The key element is a blow-up. A simple corollary is to prove the completeness of the bifurcation diagram given by Chowet al(1990 Homoclinic bifurcation at resonant eigenvalues,J. Dyn. Diff. Equ.2177-244

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《nonlinearity》 |1999年第1期|59-78|共页
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Louis-Sébastien Guimond;
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Département de Mathématiques et de Statistique, Université de Montréal, Québec, H3C 3J7, Canada, and Laboratoire de Topologie, UMR 5584 du CNRS, Université de Bourgogne, BP400, 21011 Dijon Cedex, France;

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Homoclinic loop bifurcations on a Möbius band

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