## RAMIFICATION DES SOLUTIONS DU PROBL\EME DE CAUCHY FUCHSIEN AU VOISINAGE DE L'HYPERSURFACE INITIALE

J. Math. Sci. Univ. Tokyo
Vol. 12 (2005), No. 4, Page 493--512.

PONG\'ERARD, Patrice
RAMIFICATION DES SOLUTIONS DU PROBL\EME DE CAUCHY FUCHSIEN AU VOISINAGE DE L'HYPERSURFACE INITIALE
The purpose of this paper is the decision of the domain of ramification near the initial surface $t=0$ of solutions of the Cauchy problem for a linear differential operator of Fuchs type according to Baouendi-Goulaouic. Our main result in theorem 1.1 is as follows : if, for a certain continuous function $f$, the datas are ramified in an open set of the form \$\{(t,x)\in{\bf C}\times\O ;\ |t|