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On the 65th birthday of R.Cushman

Non-Integrability of Some Painlevé VI-Equations and Dilogarithms

E. Horozov^ab, T. Stoyanova<sup>a

a</sup> Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., Sofia 1126, Bulgari
^b Institute of Mathematics and Informatics, Bulg. Acad. of Sci., Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgari

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.

Keywords: integrability, Painlevé VI-equations, Hamiltonian system.

MSC: 34M55, 37J30

Received: 12.08.2007
Accepted: 25.10.2007

Language: English

DOI: 10.1134/S1560354707060056

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