3 papers
math.DG2025
Integrable Geodesic Flows on Cones over Riemannian Manifolds
Andrey E. Mironov, Siyao Yin
In this paper we study the behavior of geodesics on cones over arbitrary -smooth closed Riemannian manifolds. We show that the geodesic flow on such cones admits first integra…
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…