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math.DS2026
Integrability of Billiards Inside Cones as a Discrete-Time Hamiltonian System
Andrey E. Mironov, Siyao Yin
In this paper, we continue to study billiards inside cones over strictly convex closed manifolds with non-degenerate second fundamental form. Recently…
math.DS2025
Billiard trajectories inside Cones
Andrey E. Mironov, Siyao Yin
Recently it was proved that every billiard trajectory inside a convex cone has a finite number of reflections. Here, by a convex cone, we mean a cone whose section with…
math.DS2025
Integrable Birkhoff Billiards inside Cones
Andrey E. Mironov, Siyao Yin
One of the most interesting problems in the theory of Birkhoff billiards is the problem of integrability. In all known examples of integrable billiards, the billiard tables are eit…