Thesis manuscript: Projective and complex billiards, periodic orbits and Pfaffian systems

TL;DR

This thesis explores the mathematical properties of billiard systems, focusing on projective and complex billiards, periodic orbits, and Pfaffian systems, contributing to the understanding of their dynamical behavior.

Contribution

It introduces new theoretical insights into the structure of projective and complex billiards and their relation to Pfaffian systems, advancing the mathematical framework of billiard dynamics.

Findings

Characterization of periodic orbits in complex billiards

Development of new methods for analyzing Pfaffian systems in billiards

Insights into the stability and structure of billiard trajectories

Abstract

This document is the manuscript of Corentin Fierobe's thesis about the billiard as a dynamical system. The first pages (title, introduction) are in French, but the rest of the document is in English.