Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






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


Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 110, 50 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.110
(Mi sigma1192)
 

This article is cited in 7 scientific papers (total in 7 papers)

Commutation Relations and Discrete Garnier Systems

Christopher M. Ormeroda, Eric M. Rainsb

a University of Maine, Department of Mathemaitcs & Statistics, 5752 Neville Hall, Room 322, Orono, ME 04469, USA
b California Institute of Technology, Mathematics 253-37, Pasadena, CA 91125, USA
Full-text PDF (703 kB) Citations (7)
References:
Abstract: We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlevé equations.
Keywords: integrable systems; difference equations; Lax pairs; discrete isomonodromy.
Funding agency Grant number
National Science Foundation DMS-1500806
The work of EMR was partially supported by the National Science Foundation under the grant DMS-1500806.
Received: March 30, 2016; in final form October 30, 2016; Published online November 8, 2016
Bibliographic databases:
Document Type: Article
MSC: 39A10; 39A13; 37K15
Language: English
Citation: Christopher M. Ormerod, Eric M. Rains, “Commutation Relations and Discrete Garnier Systems”, SIGMA, 12 (2016), 110, 50 pp.
Citation in format AMSBIB
\Bibitem{OrmRai16}
\by Christopher~M.~Ormerod, Eric~M.~Rains
\paper Commutation Relations and Discrete Garnier Systems
\jour SIGMA
\yr 2016
\vol 12
\papernumber 110
\totalpages 50
\mathnet{http://mi.mathnet.ru/sigma1192}
\crossref{https://doi.org/10.3842/SIGMA.2016.110}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000388503000001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84996497316}
Linking options:
  • https://www.mathnet.ru/eng/sigma1192
  • https://www.mathnet.ru/eng/sigma/v12/p110
  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:154
    Full-text PDF :31
    References:31
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024