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Russian Mathematical Surveys, 2004, Volume 59, Issue 6, Pages 1047–1059
DOI: https://doi.org/10.1070/RM2004v059n06ABEH000794 (Mi rm794) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Birkhoff's reduction problem

B. Balser

University of Ulm
English version PDF (199 kB) Citations (5)
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DOI: https://doi.org/10.1070/RM2004v059n06ABEH000794
Abstract: Birkhoff's reduction problem is to find an analytic or meromorphic transformation reducing a linear system of meromorphic ordinary differential equations to a form in which the coefficients are polynomials. This article is a survey of existing results, with several new results stated. In particular, it is shown that every irreducible system with an unramified formal fundamental solution can be transformed meromorphically into Birkhoff standard form, that is, to a system of minimal Poincaré rank and with normalized eigenvalues at the origin.
Received: 27.07.2004
Russian version:
Uspekhi Matematicheskikh Nauk, 2004, Volume 59, Issue 6(360), Pages 41–54
DOI: https://doi.org/10.4213/rm794
Bibliographic databases:
Document Type: Article
UDC: 517.927.71
MSC: Primary 34M35, 34C20; Secondary 34A30, 34A25, 34M05
Language: English
Original paper language: Russian
Citation: B. Balser, “Birkhoff's reduction problem”, Uspekhi Mat. Nauk, 59:6(360) (2004), 41–54; Russian Math. Surveys, 59:6 (2004), 1047–1059
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/rm/v59/i6/p41
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Успехи математических наук Russian Mathematical Surveys
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    Russian version PDF:234
    English version PDF:27
    References:79
    First page:1
     
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