On Length Spectrum Rigidity in Dispersing Billiard Systems

Speaker. Otto Vaughn Osterman
Date. 28.02.23 at 3:30 pm

Abstract. The problem of spectral rigidity in billiard systems asks whether or not, within a particular class of billiard systems, the shape of the billiard table is uniquely determined by the perimeters of the periodic orbits. We consider this problem for the class of dispersing billiard systems in the plane formed by removing three convex analytic scatterers satisfying the non-eclipse condition. My result is that the perimeters of a particular set of periodic orbits for two such systems are identical if and only if their collision maps are analytically conjugated to each other in some neighborhood of a homoclinic orbit, thus reducing the problem of marked spectral rigidity to a problem of analytic conjugacy.