Geodesic
Global Bifurcations on the Klein bottle. The Unimodal Case
Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 348-363.

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Nonlocal bifurcations of vector fields on the Klein bottle are studied. The problem is to construct a bifurcation scenario that corresponds to disappearance of a saddle-node cycle on the Klein bottle filled with homoclinic trajectories of this cycle. For the global Poincaré map specified by a unimodal function, a complete description of bifurcation scenarios is obtained. The bifurcation scenario corresponding to an arbitrary unimodal function is written out. Also, a classification of bifurcation scenarios that shows which of them can be realized in the unimodal case is given. 
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A. R. Borisyuk. Global Bifurcations on the Klein bottle. The Unimodal Case. Matematičeskie zametki, Tome 71 (2002) no. 3, pp. 348-363. http://geodesic.mathdoc.fr/item/MZM_2002_71_3_a2/

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