2025/06/23 by Li, Zaicun
#Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2506.18433
We study outer billiard systems around a class of circular sectors. For semi-discs, we prove the existence of elliptic islands occupying a positive proportion of the plane. Combined with known results, this shows the coexistence of stability and diffusion for this system. On the other hand, we show that there exists a countable family of circular sectors for which the outer billiard system has zero measure of escaping orbits.