Ergodic Theory and Dynamical Systems

Research Article

On Moser’s boundedness problem of dual Billiards


a1 School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China (email: [email protected])


In this paper, the boundedness of the dual billiard orbits of trapezoids is obtained. This gives an example showing that there are also polygons, which are neither rational nor quasi-rational, with all of their dual billiard orbits bounded. Moreover, most of the orbits are Poisson-stable, which means that most points will come sufficiently near to their original positions under iterations of the dual billiard map.

(Received September 29 2007)

(Revised April 28 2008)