(1) Institute of Mathematics and Informatics, Bulg. Acad. of Sci., Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria;(2) Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., Sofia, 1126, Bulgaria
Abstract:
The paper studies the Painlevé VIe equations from the point of view of Hamiltonian nonintegrability. For certain infinite number of points in the parameter
space we prove that the equations are not integrable. Our approach uses recent advance in Hamiltonian integrability reducing
the problem to higher differential Galois groups as well as the monodromy of dilogarithic functions.