The Poncelet Theorem and Billiards

Abstract

Usually billiards are studied in the framework of the theory of dynamical systems. My work actually emphasizes connections to the geometry and to physics, and billiards are treated here in their relation with geometrical optics. For this I studied various types of geometries like affine and projective. The main aim of my project was billiard study, their transformations and the Poncelet theorem which is consequence of the integral billiard map.