Integrable Billiards and Related Topics

Key Points

• This survey presents various integrable billiard models, including magnetic billiards and Minkowski billiards, enriching the field with diverse perspectives.
• Key findings involve a new isoperimetric-type inequality related to the Mather β-function for convex plane billiards, showcasing significant theoretical advancements.
• The analysis covers specific models like wire billiards and billiards in cones, contributing to a broad understanding of integrable dynamics in these systems.
• The conclusion raises open questions in integrable billiards, urging further exploration to deepen comprehension of the established concepts.