Λ-stability of periodic billiard orbits. (2nd August 2018) - Gaivão, José Pedro; Troubetzkoy, Serge
Abstract: We introduce a new notion of stability for periodic orbits in polygonal billiards. We say that a periodic orbit of a polygonal billiard is λ -stable if there is a periodic orbit for the corresponding pinball billiard which converges to it as . This notion of stability is unrelated to the notion introduced by Galperin, Stepin and Vorobets. We give sufficient and necessary conditions for a periodic orbit to be λ -stable and prove that the set of d -gons having at most finite number of λ -stable periodic orbits is dense is the space of d -gons. Moreover, we also determine completely the λ -stable periodic orbits in integrable polygons.