The paper studies the Painlevé VI
e 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 Painlevé VI-Equations and Dilogarithms, Regular and Chaotic Dynamics,
2007, Volume 12, Number 6,
pp. 622-629