Counting Periodic Trajectories of Finsler Billiards

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2020
• Main Authors: Blagojević, Pavle V.M., Harrison, Michael, Tabachnikov, Serge, Ziegler, Günter M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210588
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Counting Periodic Trajectories of Finsler Billiards. Pavle V.M. Blagojević, Michael Harrison, Serge Tabachnikov and Günter M. Ziegler. SIGMA 16 (2020), 022, 33 pages

We provide lower bounds on the number of periodic Finsler billiard trajectories inside a quadratically convex smooth closed hypersurface M in a 𝑑-dimensional Finsler space with possibly irreversible Finsler metric. An example of such a system is a billiard in a sufficiently weak magnetic field. The...