Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
66/1998

Qualitative aspects of classical potential scattering

Andreas Knauf

Abstract

We derive criteria for the existence of trapped orbits (orbits which are scattering in the past and bounded in the future). Such orbits exist if the boundary of Hill's region is non-empty and not homeomorphic to a sphere.

For non-trapping energies we introduce a topological degree which can be non-trivial for low energies, and for Coulombic and other singular potentials. A sum of non-trapping potentials of disjoint support is trapping iff at least two of them have non-trivial degree.

For d>=2 dimensions the potential vanishes if for any energy above the non-trapping threshold the classical differential cross section is a continuous function of the asymptotic directions.

Received:
Jan 25, 1999
Published:
Jan 25, 1999

Related publications

inJournal
1999 Repository Open Access
Andreas Knauf

Qualitative aspects of classical potential scattering

In: Regular and chaotic dynamics, 4 (1999) 1, pp. 3-22