- Oggetto:
Mathematical billiards: classical problems and recent advances
- Oggetto:
Academic year 2024/2025
- Teachers
- Irene De Blasi (Lecturer)
Stefano Baranzini (Lecturer) - Teaching period
- To be defined
- Credits/Recognition
- 4
- Delivery
- Formal authority
- Language
- English
- Attendance
- Obligatory
- Oggetto:
Sommario del corso
- Oggetto:
Program
The course is divided into two parts. Part I will cover the basics and will serve as an introduction to billiard dynamics. In Part II we plan to discuss some more advanced topics and recent developments of the theory. Part I (roughly 10 hours) will cover the following topics: Integrable billiards, Caustics and Integrability, Periodic trajectories in billiards, Symplectic twist maps, Billiards as area preserving twist maps, Symplectic and outer billiards. Part II will cover some variants of the classical Birkhoff case, including billiards with potentials, which could be of particular interest in Celestial Mechanics as well. In particular, it will include: Gravitational and Kepler Billiards, Birkhoff Billiards, Magnetic Billiards, Refraction Billiards. Depending on time and on the audience taste, the course could be enriched with additional topics, as for example some notes about local Birkhoff conjecture, dispersive billiards related to the N-body problem, or the Hyperbolicity of the system of n masses bouncing on a line under a constant force. The duration of the course is 20 hours, possibly considering to structure the final part of the course as a reading seminar.
Suggested readings and bibliography
- Oggetto:
Notes
Hours: 20- Oggetto:
