Ergodic Theory and Dynamical Systems

Research Article

On Moser’s boundedness problem of dual Billiards

LONG LIa1

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

Abstract

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)