TY - JOUR T1 - A Review on The Sixth Painlevé Equation Y1 - 2012 A1 - Davide Guzzetti KW - Painlevé equation AB -

For the Painlev\\\'e 6 transcendents, we provide a unitary description of the\r\ncritical behaviours, the connection formulae, their complete tabulation, and\r\nthe asymptotic distribution of the poles close to a critical point.

PB - SISSA UR - http://hdl.handle.net/1963/6525 N1 - 31 pages, 10 figures U1 - 6470 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - Generic T1 - The elliptic representation of the sixth Painlevé equation. T2 - Théories asymptotiques et équations de Painlevé : [colloque], Angers, juin 2004 / édité par Éric Delabaere, Michèle Loday-Richaud. - Paris : Société mathématique de France, 2006. - Collection SMF. Séminaires et congrès. - page : 83-101 Y1 - 2004 A1 - Davide Guzzetti KW - Painlevé equation AB - We find a class of solutions of the sixth Painlev´e equation corresponding\r\nto almost all the monodromy data of the associated linear system; actually, all data\r\nbut one point in the space of data. We describe the critical behavior close to the\r\ncritical points by means of the elliptic representation, and we find the relation among\r\nthe parameters at the different critical points (connection problem). JF - Théories asymptotiques et équations de Painlevé : [colloque], Angers, juin 2004 / édité par Éric Delabaere, Michèle Loday-Richaud. - Paris : Société mathématique de France, 2006. - Collection SMF. Séminaires et congrès. - page : 83-101 PB - Societe Matematique de France SN - 978-2-85629-229-7 UR - http://hdl.handle.net/1963/6529 U1 - 6482 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER - TY - CHAP T1 - Stokes Matrices for Frobenius Manifolds and the 6 Painlevé Equation T2 - Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109 Y1 - 2000 A1 - Davide Guzzetti KW - Painlevé equation AB - These notes are a short review on the theory of Frobenius manifolds and its connection to problems of isomonodromy deformations and to Painlev'e equations. JF - Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109 PB - Kobe University, Japan SN - 4-907719-07-8 UR - http://hdl.handle.net/1963/6546 U1 - 6478 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER -