Non-Integrability of Some Painlevé VI-Equations and Dilogarithms

    2007, Volume 12, Number 6, pp.  622-629

    Author(s): Horozov E., Stoyanova C.

    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
    Citation: Horozov E., Stoyanova C., Non-Integrability of Some PainlevĂ© VI-Equations and Dilogarithms, Regular and Chaotic Dynamics, 2007, Volume 12, Number 6, pp. 622-629

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