5 J. Bourchier Blvd., Sofia 1126, Bulgaria
Department of Mathematics and Informatics, Sofia University
Horozov E., Stoyanova C.
Non-Integrability of Some Painlevé VI-Equations and Dilogarithms
2007, vol. 12, no. 6, pp. 622-629
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.