Andreas Knauf
Qualitative Aspects of Classical Potential Scattering
(62K, LaTeX)

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 $d\geq 2$ 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.