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Journal of Mathematical Physics / Volume 53 / Issue 2 / ARTICLES / Dynamical Systems

J. Math. Phys. 53, 022701 (2012); http://dx.doi.org/10.1063/1.3681897 (15 pages)

The holonomy group at infinity of the Painlevé VI equation

Bassem Ben Hamed1, Lubomir Gavrilov2, and Martine Klughertz2

1Institut Supérieur des Sciences Appliquées et de Technologie de Gabès, Département de Mathématiques, Rue Amor Ben El Khatab, 6029 Gabès, Tunisia
2Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, 31062 Toulouse, France

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(Received 10 April 2011; accepted 13 January 2012; published online 3 February 2012)

We prove that the holonomy group at infinity of the Painlevé VI equation is virtually commutative.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE OKAMOTO COMPACTIFICATION
  3. HIGHER ORDER VARIATIONAL EQUATIONS AND THEIR MONODROMY GROUPS
    1. The first variational equation
    2. The second variational equation
  4. THE HOLONOMY AT INFINITY

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KEYWORDS and PACS

Keywords

differential equations

PACS

  • 02.30.Hq

    Ordinary differential equations

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3681897

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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