TY - JOUR
T1 - Solving the Sixth PainlevĂ© Equation: Towards the Classification of all the Critical Behaviors and the Connection Formulae
JF - Int Math Res Notices (2012) 2012 (6): 1352-1413
Y1 - 2012
A1 - Davide Guzzetti
AB - The critical behavior of a three real parameter class of solutions of the\\r\\nsixth Painlev\\\\\\\'e equation is computed, and parametrized in terms of monodromy\\r\\ndata of the associated $2\\\\times 2$ matrix linear Fuchsian system of ODE. The\\r\\nclass may contain solutions with poles accumulating at the critical point. The\\r\\nstudy of this class closes a gap in the description of the transcendents in one\\r\\nto one correspondence with the monodromy data. These transcendents are reviewed in the paper. Some formulas that relate the monodromy data to the critical behaviors of the four real (two complex) parameter class of solutions are\\r\\nmissing in the literature, so they are computed here. A computational procedure to write the full expansion of the four and three real parameter class of solutions is proposed.
PB - Oxford University Press
UR - http://hdl.handle.net/1963/6093
N1 - 53 pages, 2 figures
U1 - 5979
U2 - Mathematics
U3 - Mathematical Physics
U4 - -1
ER -