 9343 Petkov V., Stoyanov L.
 Sojourn times of trapping rays and the behaviour of the
modified resolvent of the Laplacian
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Feb 22, 93

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Abstract. Let K be an obstacle in an odddimensional Euclidean space
which is a finite disjoint union of convex bodies with smooth boundaries.
Assuming that there are no nontrivial open subsets of the boundary
where the Gauss curvature vanishes, it is shown that there exists a
sequence of scattering rays in the complement Q of K such that the
corresponding sequence of sojourn times tends to infinity and consists
of singularities of the scattering kernel. Using this, certain
information on the behaviour of the modified resolvent of the Laplacian
and the distribution of poles of the scattering matrix is obtained.
For the same kind of obstacles K, without the additional assumption
on the Gauss curvature, it is established that for almost all pairs
(a,b) of unit vectors all singularities of the scattering kernel
s(t,a,b) are related to sojourn times of reflecting (a,b)rays in Q.
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