33 citations · 136 across the 39 of their papers we have counts for
41 papers
On differential equations of integrable billiard tables
Vladimir Dragović, Andrey E. Mironov
We introduce a method to find differential equations for functions which define tables, such that associated billiard systems admit a local first integral. We illustrate this metho…
The Birkhoff-Poritsky conjecture for centrally-symmetric billiard tables
Misha Bialy, Andrey E. Mironov
In this paper we prove the Birkhoff-Poritsky conjecture for centrally-symmetric -smooth convex planar billiards. We assume that the domain between the invariant c…
Magnetic billiards: Non-integrability for strong magnetic field; Gutkin type examples
Misha Bialy, Andrey E. Mironov, Lior Shalom
We consider magnetic billiards under a strong constant magnetic field. The purpose of this paper is two-folded. We examine the question of existence of polynomial integral of billi…
Periodic one-point rank one commuting difference operators
Alina Dobrogowska, Andrey E. Mironov
In this paper we study one-point rank one commutative rings of difference operators. We find conditions on spectral data which specify such operators with periodic coefficients.
Wire billiards, the first steps
Misha Bialy, Andrey Mironov, Serge Tabachnikov
Wire billiard is defined by a smooth embedded closed curve of non-vanishing curvature in (a wire). For a class of curves, that we call nice wires, the wire billi…
Outer billiards with the dynamics of a standard shift on a finite number of invariant curves
Misha Bialy, Andrey E. Mironov, Lior Shalom
We give a beautiful explicit example of a convex plane curve such that the outer billiard has a given finite number of invariant curves. Moreover, the dynamics on these curves is a…