The equations for geodesic flow on the ellipsoid are well known, and were first solved by Jacobi in 1838 by separating the variables of the Hamilton-Jacobi equation. In 1979 Moser investigated theâ€¦ (More)

The purpose of this paper is to discuss the relationship between commutative and non-commutative integrability of Hamiltonian systems and to construct new examples of integrable geodesic flows onâ€¦ (More)

A formal Frobenius theorem, which is an analog of the classical integrability theorem for smooth distributions, is proved and applied to generalize the argument shift method of A. S. Mishchenko andâ€¦ (More)

such that i) the geodesic flow on MA is (Liouville) integrable by C âˆž first integrals; ii) the geodesic flow on MA is not (Liouville) integrable by real-analytic first integrals; iii) the topologicalâ€¦ (More)

Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this 3-manifold (if itâ€¦ (More)

We describe a class of completely integrable G-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group G with magnetic field given by the Kirillov-Konstant 2-form.

1) Classificaton of the algebra of n vortices on a plane 2) Solvable problems of vortex dynamics 3) Algebraization and reduction in a three-body problem Abstract The work [13] introduces a naiveâ€¦ (More)

For any finite-dimensional Lie algebra we introduce the notion of JordanKronecker invariants, study their properties and discuss examples. These invariants naturally appear in the framework of theâ€¦ (More)