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.

}, keywords = {Painlev{\'e} equation}, url = {http://hdl.handle.net/1963/6525}, author = {Davide Guzzetti} } @proceedings {2004, title = {The elliptic representation of the sixth Painlev{\'e} equation.}, year = {2004}, publisher = {Societe Matematique de France}, abstract = {We find a class of solutions of the sixth Painlev{\textasciiacute}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).}, keywords = {Painlev{\'e} equation}, isbn = {978-2-85629-229-7}, url = {http://hdl.handle.net/1963/6529}, author = {Davide Guzzetti} } @inbook {2000, title = {Stokes Matrices for Frobenius Manifolds and the 6 Painlev{\'e} Equation}, booktitle = {Rokko Lectures in Mathematics, Vol 7 [Issue title: Perspective of Painleve equations], (2000), pages : 101-109}, number = {Rokko lectures in mathematics;vol. 7}, year = {2000}, publisher = {Kobe University, Japan}, organization = {Kobe University, Japan}, abstract = {These notes are a short review on the theory of Frobenius manifolds and its connection to problems of isomonodromy deformations and to Painlev{\textquoteright}e equations.}, keywords = {Painlev{\'e} equation}, isbn = {4-907719-07-8}, url = {http://hdl.handle.net/1963/6546}, author = {Davide Guzzetti} }