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math.DS2026
Existence of stable periodic orbits in billiards close to lemon and moon billiards
Alexander Grigo
It is known that at lemon and moon billiards that have a sufficiently small curvature on one of their circular arcs are hyperbolic. In this paper we show that replacing this circul…
math.DS2018
A rigorous derivation of Haff's law for a periodic two-disk fluid
Alexander Grigo
We derive Haff's cooling law for a periodic fluid consisting of two hard disks per unit cell by reducing it to a point particle moving inside a Sinai billiard with finite horizon w…
math.DS2018
How smooth can convex chaotic billiard tables be?
Leonid Bunimovich, Alexander Grigo
We solve the longstanding problem of smoothing a stadium billiard. Besides our results demonstrate why there were no clear conjectures how much the stadium's boundary must be smoot…