A canonical form of a system of microdifferential equations with non-involutory characteristics and branching of singularities

Abstract

We study a system ℳ of microdifferential (=pseudodifferential) equations. We assume that the characteristic varietyV of ℳ takes the formV=V 1∪V2; hereV 1andV 2are regular involutory submanifolds and intersect normally, andV 1∩V2is non-involutory and 1-codimensional both inV 1and inV 2. We also assume that ℳ has regular singularities alongV. Then we give a canonical form of ℳ in the complex domain. This enables us to investigate the branching of supports of microfunction solutions of ℳ when ℳ is hyperbolic.