RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2007, Volume 81, Issue 4, Pages 599–613 (Mi mz3702)  

This article is cited in 5 scientific papers (total in 5 papers)

General Linear Problem of the Isomonodromic Deformation of Fuchsian Systems

V. A. Poberezhnyi

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: In contrast to nonresonance systems whose continuous deformations are always Schlesinger deformations, systems with resonances provide great possibilities for deformations. In this case, the number of continuous parameters of deformation, in addition to the location of the poles of the system, includes the data describing the Levelt structure of the system, or, in other words, the distribution of resonance directions in the space of solutions. The question of classifying the form and structure of deformations according to these parameters arises. In the present paper, we consider continuous isomonodromic deformations of Fuchsian systems, including those with respect to additional parameters, describe the corresponding linear problem, and present the Pfaff form of the linear problem of general continuous isomonodromic deformation of Fuchsian systems.

Keywords: Fuchsian equations and systems, isomonodromic deformation, Levelt normalization, gauge transformation, resonance singular point, Pfaff form

DOI: https://doi.org/10.4213/mzm3702

Full text: PDF file (526 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2007, 81:4, 529–542

Bibliographic databases:

UDC: 517.9+514.745.8
Received: 04.10.2006

Citation: V. A. Poberezhnyi, “General Linear Problem of the Isomonodromic Deformation of Fuchsian Systems”, Mat. Zametki, 81:4 (2007), 599–613; Math. Notes, 81:4 (2007), 529–542

Citation in format AMSBIB
\Bibitem{Pob07}
\by V.~A.~Poberezhnyi
\paper General Linear Problem of the Isomonodromic Deformation of Fuchsian Systems
\jour Mat. Zametki
\yr 2007
\vol 81
\issue 4
\pages 599--613
\mathnet{http://mi.mathnet.ru/mz3702}
\crossref{https://doi.org/10.4213/mzm3702}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2352025}
\zmath{https://zbmath.org/?q=an:1138.34043}
\elib{http://elibrary.ru/item.asp?id=9486228}
\transl
\jour Math. Notes
\yr 2007
\vol 81
\issue 4
\pages 529--542
\crossref{https://doi.org/10.1134/S0001434607030303}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000246269000030}
\elib{http://elibrary.ru/item.asp?id=13562047}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248325552}


Linking options:
  • http://mi.mathnet.ru/eng/mz3702
  • https://doi.org/10.4213/mzm3702
  • http://mi.mathnet.ru/eng/mz/v81/i4/p599

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Poberezhny V., “On the Painlevé property of isomonodromic deformations of Fuchsian systems”, Acta Appl. Math., 101:1-3 (2008), 255–263  crossref  mathscinet  zmath  isi  elib  scopus
    2. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations”, Russian Math. Surveys, 66:1 (2011), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. R. R. Gontsov, V. A. Poberezhnyi, G. F. Helminck, “On deformations of linear differential systems”, Russian Math. Surveys, 66:1 (2011), 63–105  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Yulia Bibilo, Galina Filipuk, “Non-Schlesinger Isomonodromic Deformations of Fuchsian Systems and Middle Convolution”, SIGMA, 11 (2015), 023, 14 pp.  mathnet  crossref  mathscinet
    5. Davide Guzzetti, “Notes on Non-Generic Isomonodromy Deformations”, SIGMA, 14 (2018), 087, 34 pp.  mathnet  crossref
  • Математические заметки Mathematical Notes
    Number of views:
    This page:351
    Full text:109
    References:32
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019