Andrey E. Mironov

Commuting Ordinary Differential Operators with Polynomial Coefficients and Automorphisms of the First Weyl Algebra

In this paper we study rank two commuting ordinary differential operators with polynomial coefficients and the orbit space of the automorphisms group of the first Weyl algebra on such operators. We prove that for arbitrary fixed spectral curve of genus one the space of orbits is infinite. Moreover, we prove in this case that for for any

Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs

nge 1

Algebraic non-integrability of magnetic billiards

there is a pair of self-adjoint commuting ordinary differential operators of rank two

Baker-Akhiezer Modules on Rational Varieties

L_4=(partial_x^2+V(x))^2+W(x)

A survey on polynomial in momenta integrals for billiard problems

,

In search of periodic solutions for a reduction of the Benney chain

L_{6}

Rich quasi-linear system for integrable geodesic flows on 2-torus

, where

Angular billiard and algebraic Birkhoff conjecture

W(x),V(x)

Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane

are polynomials of degree

Integrable geodesic flows on 2-torus: Formal solutions and variational principle

n