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Théories Asymptotiques et Équations de Painlevé
Edited by: Éric Delabaere and Michèle Loday-Richaud, Université d'Angers, France
A publication of the Société Mathématique de France.
Séminaires et Congrès
2007; 363 pp; softcover
Number: 14
ISBN-10: 2-85629-229-1
ISBN-13: 978-2-85629-229-7
List Price: US$110
Member Price: US$88
Order Code: SECO/14
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The major part of this volume is devoted to the study of the sixth Painlevé equation through a variety of approaches, namely elliptic representation, the classification of algebraic solutions and so-called "dessins d'enfants" deformations, affine Weyl group symmetries and dynamics using the techniques of Riemann-Hilbert theory and those of algebraic geometry.

Discrete Painlevé equations and higher order equations, including the mKdV hierarchy and its Lax pair and a WKB analysis of perturbed Noumi-Yamada systems, are given a place of study, as well as theoretical settings in Galois theory for linear and non-linear differential equations, difference and \(q\)-difference equations with applications to Painlevé equations and to integrability or non-integrability of certain Hamiltonian systems.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in number theory.

Table of Contents

  • P. Boalch -- Six results on Painlevé VI
  • P. A. Clarkson -- Special polynomials associated with rational and algebraic solutions of the Painlevé equations
  • P. A. Clarkson, N. Joshi, and M. Mazzocco -- The Lax pair for the mKdV hierarchy
  • R. Conte, M. Musette, and C. Verhoeven -- Painlevé property of the Hénon- Heiles Hamiltonians
  • D. Guzzetti -- The elliptic representation of the sixth Painlevé equation
  • M. Inaba, K. Iwasaki, and M.-H. Saito -- Dynamics of the sixth Painlevé equation
  • K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta, and Y. Yamada -- Point configurations, Cremona transformations and the elliptic difference Painlevé equation
  • A. V. Kitaev -- Remarks toward a classification of \(RS^2_4(3)\)-transformations and algebraic solutions of the sixth Painlevé equation
  • J. Morales-Ruiz -- A remark about the Painlevé transcendents
  • A. Ramani, B. Grammaticos, and T. Tamizhmani -- On the alternate discrete Painlevé equations and related systems
  • J. Sauloy -- Isomonodromy for complex linear \(q\)-difference equations
  • Y. Takei -- On a local reduction of a higher order Painlevé equation and its underlying Lax pair near a simple turning point of the first kind
  • H. Umemura -- Galois theory and Painlevé equations
  • C. Zhang -- Solutions asymptotiques et méromorphes d'equations aux \(q\)-différences
  • Programme
  • Liste des participants
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