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Propagation of singularities in three-body scattering. (English) Zbl 0941.35001
Astérisque. 262. Paris: Société Mathématique de France. iv, 151 p. (2000).
In this memoire the author considers a compact manifold with boundary $$X$$ equipped with a scattering metric $$g$$ and with a collection $$c_i$$ of disjoint closed embedded submanifolds of $$\partial X$$. Let $$\Delta$$ be the Laplacian of $$g$$, suppose that $$V\in C^\infty ([X_i\cup_iC_i])$$ where $$[X_i \cup_iC_i]$$ is $$X$$ blown up along $$C_i$$, assume that $$V$$ vanishes at the lift of $$\partial X$$, and consider the operator $$H=\Delta+V$$. The author analyzes the propagation of singularities of generalized eigenfunctions of $$H$$, showing that this is essentially a hyperbolic problem which has much in common with the Dirichlet and transmission problems for the wave operator. The author shows also that the wave front relation of the free-to-free part of the scattering matrix is given by the broken geodesic flow at distance $$\pi$$.
Reviewer: N.Jacob (Erlangen)

##### MSC:
 35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations 35P25 Scattering theory for PDEs 81U10 $$n$$-body potential quantum scattering theory