| Автор | Louis-Sébastien Guimond |
| Дата выпуска | 1999-01-01 |
| dc.description | 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 triviaux 7 1349-65) 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 Chow et al (1990 Homoclinic bifurcation at resonant eigenvalues, J. Dyn. Diff. Equ. 2 177-244). |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Homoclinic loop bifurcations on a Möbius band |
| Тип | paper |
| DOI | 10.1088/0951-7715/12/1/005 |
| Electronic ISSN | 1361-6544 |
| Print ISSN | 0951-7715 |
| Журнал | Nonlinearity |
| Том | 12 |
| Первая страница | 59 |
| Последняя страница | 78 |
| Аффилиация | Louis-Sébastien Guimond; 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 |
| Выпуск | 1 |
