论文信息 - Middle convolution and deformation for Fuchsian systems

Middle convolution and deformation for Fuchsian systems

Middle convolution and addition are operations for Fuchsian systems of differential equations which preserve the number of accessory parameters. In this paper we show that they also preserve the deformation equations. Several Bäcklund transformations of the sixth Painlevé equation are obtained from this viewpoint.

Y. Haraoka | G. Filipuk

[1] D. Novikov. Integral transformation of solutions for a Fuchsian-class equation corresponding to the Okamoto transformation of the Painlevé VI equation , 2006 .

[2] G. Filipuk. On the middle convolution and birational symmetries of the sixth Painleve equation , 2006 .

[3] P. Boalch. Painleve Equations and Complex Reflections , 2013, 1305.6462.

[4] P. Boalch. From Klein to Painlevé Via Fourier, Laplace and Jimbo , 2003, math/0308221.

[5] M. Dettweiler,et al. On the middle convolution , 2003, math/0305311.

[6] M. Mazzocco. Painlevé sixth equation as isomonodromic deformations equation of an irregular system , 2002 .

[7] Stefan Reiter,et al. An Algorithm of Katz and its Application to the Inverse Galois Problem , 2000, J. Symb. Comput..

[8] N. Hitchin. Geometrical aspects of Schlesinger's equation , 1997 .

[9] J. Harnad. Dual isomonodromic deformations and moment maps to loop algebras , 1993, hep-th/9301076.

[10] M. Jimbo,et al. Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II , 1981 .

[11] L. Schlesinger. Über eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten. , 1912 .