MONODROMY GROUPS OF SYSTEMS OF TOTAL DIFFERENTIAL-EQUATIONS OF 2 VARIABLES

Fuchsian systems of ordinary differential equations that are irreducib le and free from accessory parameters are classified into eight classe s. Canonical systems of these classes were determined by Haraoka [SIAM J. Math. Anal., 25 (1994), pp. 1203-1226]. Among them the canonical s ystems of exactly four classes are extended to the completely integrab le systems of total differential equations of two variables that are i ntroduced by Yokoyama [Funkcial. Ekvac., 35 (1992), pp. 65-93]. This p aper presents monodromy groups of the four systems of total differenti al equations. The theory for computing monodromy groups of the systems developed by Yokoyama is applied.