Skip Navigation


Proceedings of the London Mathematical Society Advance Access originally published online on December 6, 2006
Proceedings of the London Mathematical Society 2007 94(2):443-474; doi:10.1112/plms/pdl012
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
94/2/443    most recent
pdl012v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (5)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Halburd, R. G.
Right arrow Articles by Korhonen, R. J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2006 London Mathematical Society

Finite-order meromorphic solutions and the discrete Painlevé equations

R. G. Halburd1 and R. J. Korhonen2

1 Department of Mathematical Sciences
Loughborough University
Loughborough
Leicestershire
LE11 3TU
United Kingdom
R.G.Halburd{at}lboro.ac.uk
2 Department of Mathematics
University of Joensuu
P.O. Box 111
FI-80101 Joensuu
Finland
risto.korhonen{at}joensuu.fi

Received 24 February 2005. Revision received 24 April 2006.

Let w(z) be an admissible finite-order meromorphic solution of the second-order difference equation


Formula 012UM1

where R(z, w(z)) is rational in w(z) with coefficients that are meromorphic in z. Then either w(z) satisfies a difference linear or Riccati equation or else the above equation can be transformed to one of a list of canonical difference equations. This list consists of all known difference Painlevé equations of the above form, together with their autonomous versions. This suggests that the existence of finite-order meromorphic solutions is a good detector of integrable difference equations.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?


This article has been cited by other articles:


Home page
 Int Math Res NoticesHome page
R. G. Halburd and N. J. Southall
Tropical Nevanlinna Theory and Ultradiscrete Equations
Int Math Res Notices, January 1, 2009; 2009(5): 887 - 911.
[Abstract] [Full Text] [PDF]


Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.