5 citations · 13 across the 10 of their papers we have counts for
10 papers
A survey on Polynomial in momenta integrals for billiard problems
Michael, Bialy, Andrey E. Mironov
In this paper we give a short survey of recent results on algebraic version of the Birkhoff conjecture for integrable billiards on surfaces of constant curvature. We also discuss i…
On Newton equations which are totally integrable at infinity
Michael, Bialy
In this paper Hamiltonian system of time dependent periodic Newton equations is studied. It is shown that for dimensions and higher the following rigidity results holds true: I…
Effective bounds in E.Hopf rigidity for billiards and geodesic flows
Michael, Bialy
In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set $\mathcal{M…
Integrable geodesic flows on 2-torus: formal solutions and variational principle
Michael, Bialy, Andrey E. Mironov
In this paper we study quasi-linear system of partial differential equations which describes the existence of the polynomial in momenta first integral of the integrable geodesic fl…
A remark on the number of invisible directions for a smooth Riemannian metric
Michael, Bialy
In this note we give a construction of a smooth Riemannian metric on R^n which is standard Euclidean outside a compact set K and such that it has N = n(n + 1)=2 invisible direction…
On Totally integrable magnetic billiards on constant curvature surface
Michael, Bialy
We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrab…