Rational dual billiards. (Q1871650)

The paper investigates the dual billiard, or antibilliard, associated with a convex polygon. Using elementary geometric arguments it is proved that all orbits of the dual billiard are periodic if the convex polygon is rational. The proof also yields boundedness of all orbits in case the convex polygon is quasirational. The presentation follows mainly \textit{E. Gutkin} and \textit{N. Simanyi} [Commun. Math. Phys. 143, 431-449 (1992; Zbl 0749.58032)]. Similar results have also been obtained by \textit{R. Kołodziej} [Bull. Pol. Acad. Sci., Math. 37, 163-168 (1989; Zbl 0762.58021)].