8 citations · 17 across the 9 of their papers we have counts for
10 papers
Integrable Outer billiards and rigidity
Michael Bialy
In the present paper we introduce a new generating function for outer billiards in the plane. Using this generating function, we prove the following rigidity result: if the vicinit…
Mather -function for ellipses and rigidity
Michael Bialy
The goal of the first part of this note is to get an explicit formula for rotation number and Mather -function for ellipse. This is done here with the help of non-standard gener…
In search of periodic solutions for a reduction of the Benney chain
Michael, Bialy, Andrey Mironov
We search for smooth periodic solutions for the system of quasi-linear PDEs known as the Lax dispersionless reduction of the Benney moments chain. It is naturally related to the ex…
Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane
Michael, Bialy, Andrey E. Mironov
We consider a convex curve lying on the Sphere or Hyperbolic plane. We study the problem of existence of polynomial in velocities integrals for Birkhoff billiard inside the dom…
Angular Billiard and Algebraic Birkhoff conjecture
Michael Bialy, Andrey E. Mironov
In this paper we introduce a new dynamical system which we call Angular billiard. It acts on the exterior points of a convex curve in Euclidean plane. In a neighborhood of the boun…
From polynomial integrals of Hamiltonian flows to a model of non-linear elasticity
Michael Bialy, Andrey E. Mironov
We prove non existence of smooth solutions of a quasi-linear system suggested by Ericksen in a model of Nonlinear Elasticity. This system is of mixed elliptic-hyperbolic type. We d…