Break-up of resonant invariant circles in perturbations of the geodesic circular billiard on surfaces of constant curvature

Abstract

We study the non-persistence of horizontal invariant circles for geodesically convex perturbations of the geodesic circular billiard on surfaces of constant curvature and show that the result obtained by Ram\'irez-Ros for the planar case, remains true for billiards on surfaces with constant curvature.