Relations between second-order Fuchsian equations and first-order Fuchsian systems (Q2307969)

The authors of this work consider connections between second-order Fuchsian equations and first-order Fuchsian systems. As a results, authors reveal the links between the two approaches for the description of the Painleve VI equation: one is based on the second-order Fuchsian equation with four singularities and the other is based on an apropriate Fuchsian first-order system. The authors believe that these links simplify comparing the theory of Painleve transcendents and the theory of Heun functions.