Dual billiards, Fagnano orbits and regular polygons

Serge Troubetzkoy (1, 2, 3)

1 IML - Institut de mathématiques de Luminy
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

We study the notion of Fagnano orbits for dual polygonal billiards. We used them to characterize regular polygons and we study the iteration of the developing map.

Domaines: Systèmes dynamiques [math.DS]

Serge Troubetzkoy. Dual billiards, Fagnano orbits and regular polygons. The American Mathematical Monthly, 2009, 116, pp.251-260. ⟨hal-00139790v3⟩