Dual billiards

Abstract

CONTENTS Introduction § 1. Bisecting property § 2. Generating function and periodic points § 3. Several modifications of the dual billiard map § 4. Duality between billiards and dual billiards § 5. A theorem of Poncelet and dual billiards § 6. Integrability § 7. Affine parametrization and explicit formulae § 8. Area spectrum § 9. Invariant curves §10. Dual billiard map at infinity §11. Polygonal dual billiards §12. Affine-regular pentagon §13. Higher-dimensional dual billiards References