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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2011 Volume 66, Issue 1(397), Pages 65–110 (Mi rm9404)

This article is cited in 6 papers

On deformations of linear differential systems

R. R. Gontsova, V. A. Poberezhnyib, G. F. Helminckc

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
c Korteweg–de Vries Institute for Mathematics, University of Amsterdam, The Netherlands

Abstract: This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical results established for isomonodromic deformations of Fuchsian systems are generalized to the case of integrable deformations of meromorphic systems.
Bibliography: 40 titles.

Keywords: holomorphic bundle, meromorphic connection, integrability, monodromy, Painlevé property, isomonodromic deformation.

UDC: 517.927.7+517.936

MSC: Primary 34M35, 34M50, 53C07; Secondary 32G34, 34M55

Received: 07.12.2010

DOI: 10.4213/rm9404


 English version:
Russian Mathematical Surveys, 2011, 66:1, 63–105

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© Steklov Math. Inst. of RAS, 2024