This article is cited in 4 papers

Global Bifurcations on the Klein bottle. The Unimodal Case

A. R. Borisyuk

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 514.747

Received: 17.01.2001
Revised: 08.10.2001

DOI: 10.4213/mzm351

 English version: Mathematical Notes, 2002, 71:3, 316–329

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