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Matematicheskie Zametki, 2002, Volume 71, Issue 3, Pages 348–363
DOI: https://doi.org/10.4213/mzm351 (Mi mzm351) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Global Bifurcations on the Klein bottle. The Unimodal Case

A. R. Borisyuk

M. V. Lomonosov Moscow State University
Full-text PDF (278 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm351
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.
Received: 17.01.2001
Revised: 08.10.2001
English version:
Mathematical Notes, 2002, Volume 71, Issue 3, Pages 316–329
DOI: https://doi.org/10.1023/A:1014946223033
Bibliographic databases:
UDC: 514.747
Language: Russian
Citation: A. R. Borisyuk, “Global Bifurcations on the Klein bottle. The Unimodal Case”, Mat. Zametki, 71:3 (2002), 348–363; Math. Notes, 71:3 (2002), 316–329
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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