Advances in Mathematical Physics
Volume 2010 (2010), Article ID 941560, 44 pages
doi:10.1155/2010/941560
Research Article

Renormalization, Isogenies, and Rational Symmetries of Differential Equations

A. Bostan,1 S. Boukraa,2 S. Hassani,3 J.-M. Maillard,4 J.-A. Weil,5 N. Zenine,3 and N. Abarenkova6

1INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
2LPTHIRM and Département d'Aéronautique, Université de Blida, 09470 Blida, Algeria
3Centre de Recherche Nucléaire d'Alger, 2 Boulevard. Frantz Fanon, BP 399, 16000 Alger, Algeria
4LPTMC, UMR 7600 CNRS, Université de Paris, Tour 24, 4ème étage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05, France
5XLIM, Université de Limoges, 123 avenue Albert Thomas, 87060 Limoges Cedex, France
6St Petersburg Department of Steklov Institute of Mathematics, 27 Fontanka, 191023 St. Petersburg, Russia

Received 21 December 2009; Accepted 17 January 2010

Academic Editor: Richard Kerner

Copyright © 2010 A. Bostan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give an example of infinite-order rational transformation that leaves a linear differential equation covariant. This example can be seen as a nontrivial but still simple illustration of an exact representation of the renormalization group.