Sojourn times of trapping rays and the behaviour of the modified resolvent of the Laplacian

A. Petkov, L. Stoyanov

Research output: Contribution to journalArticle

Abstract

Obstacles K in an odd-dimensional Euclidean space are considered which are finite disjoint unions of convex bodies with smooth boundaries. Assuming that there are no non-trivial open subsets of partial derivative K where the Gauss curvature vanishes, it is shown that there exists a sequence of scattering rays in the complement Omega 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 behavior of the modified resolvent of the Laplacian and the distribution of poles of the scattering matrix is obtained. Fbr the same kind of obstacles K, without the additional assumption on the Gauss curvature, it is established that for almost all pairs (omega, theta) of unit vectors all singularities of the scattering kernel s (t, omega, theta) are related to sojourn times of reflecting (omega, theta)-rays in Omega.

Original languageEnglish
Pages (from-to)17-45
Number of pages29
JournalAnnales de L Institute Henri Poincare-Physique Theorique
Volume62
Issue number1
Publication statusPublished - 1995

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