Counting Periodic Trajectories of Finsler Billiards

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2020
• Hauptverfasser: Blagojević, Pavle V.M., Harrison, Michael, Tabachnikov, Serge, Ziegler, Günter M.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/210588
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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...