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Izvestiya: Mathematics, 2013, Volume 77, Issue 2, Pages 253–270
DOI: https://doi.org/10.1070/IM2013v077n02ABEH002635 (Mi im7984) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Asymptotics of the monodromy transformation in certain classes of monodromy germs

A. S. Voronin, N. B. Medvedeva

Chelyabinsk State University
English version PDF (320 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM2013v077n02ABEH002635
Abstract: We calculate the second term of the asymptotics of the monodromy transformation of a monodromic singular point of an analytic vector field on a plane whose Newton diagram consists of one or two edges. In the cases under consideration the principal term of the monodromy transformation coincides with the identity function. The case of two edges is characterized by the fact that, as a result of blowing up the singularity by the Newton diagram, a singular point emerges that is a degenerate saddle. The results obtained make it possible to state a sufficient condition for the existence of a focus and to construct the stability boundary in the classes of vector fields under consideration.
Keywords: monodromic singular point, blowing up singularities, focus, centre, monodromy transformation.
Funding agency Grant number
Russian Foundation for Basic Research 10-01-00587-а
Ministry of Education and Science of the Russian Federation 02.740.110612
Received: 29.03.2012
Revised: 04.07.2012
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 2, Pages 35–52
DOI: https://doi.org/10.4213/im7984
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 37C10, 34C05, 34D20, 58K45
Language: English
Original paper language: Russian
Citation: A. S. Voronin, N. B. Medvedeva, “Asymptotics of the monodromy transformation in certain classes of monodromy germs”, Izv. RAN. Ser. Mat., 77:2 (2013), 35–52; Izv. Math., 77:2 (2013), 253–270
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:165
    English version PDF:8
    References:45
    First page:16
     
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