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Deuxième microlocalisation sur les sous variétés isotropes. (French) Zbl 0539.58038
In this paper, we construct the second micro-support of a distribution on $$R^ n$$, with respect to an isotropic subvariety $$\Gamma$$ of $$T^*R^ n$$. It is a closed set in a fiber bundle $${\tilde \Gamma}$$ over $$\Gamma$$, which is canonically a symplectic variety, and which contains the cotangent bundle of $$\Gamma$$. We prove the Watermelon theorem and apply our result to the study of the propagation of singularities of solutions, defined on an open set $$\Omega$$, of a differential operator P of real principal type, near a bicharacteristic curve of P, contained in the boundary of $$\Omega$$.

##### MSC:
 58J47 Propagation of singularities; initial value problems on manifolds
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##### References:
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