(1) Department of Mathematics, Technion Israel Institute of Technology, Haifa, Israel
Abstract:
We construct examples of pairs of surfaces that share the same poles (with multiplicity) of the scattering operatorm, and that are particularly simple in one or more senses. In particular, we find pairs of isoscattering surfaces of small genus with a small number of ends. We also give examples of congruence surfaces which are isoscattering.