Katz’s middle convolution and Yokoyama’s extending operation. (English) Zbl 1326.34133
A Fuchsian system is a linear system of ordinary differential equations on Riemann’s sphere having only logarithmic poles. When the conjugacy classes of the tuple of matrices-residua (resp. of monodromy operators) define the tuple up to conjugacy, the former is said to be rigid. In the rigid case the author provides a concrete relation between Katz’s middle convolution and Yokoyama’s extension and shows the equivalence of these operations. In this context he mentions results of Dettweiler and Reiter, Crawley-Boevey, Haraoka, Kostov, Oshima and the Okubo normal form for Fuchsian systems.
Reviewer: Vladimir P. Kostov (Nice)
MSC:
34M35 | Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms |
34M40 | Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain |
34M15 | Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain |