Séminaires et Congrès 2007; 363 pp; softcover Number: 14 ISBN10: 2856292291 ISBN13: 9782856292297 List Price: US$110 Member Price: US$88 Order Code: SECO/14
 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 socalled "dessins d'enfants" deformations, affine Weyl group symmetries and dynamics using the techniques of RiemannHilbert 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 NoumiYamada systems, are given a place of study, as well as theoretical settings in Galois theory for linear and nonlinear differential equations, difference and \(q\)difference equations with applications to Painlevé equations and to integrability or nonintegrability 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. Readership 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. MoralesRuiz  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
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