12 citations · 48 across the 26 of their papers we have counts for
5 papers · 1 filter
Curvature of Poisson pencils in dimension three
Anton Izosimov
A Poisson pencil is called flat if all brackets of the pencil can be simultaneously locally brought to a constant form. Given a Poisson pencil on a 3-manifold, we study under which…
Stability of relative equilibria of multidimensional rigid body
Anton Izosimov
It is a classical result of Euler that the rotation of a torque-free three-dimensional rigid body about the short or the long axis is stable, whereas the rotation about the middle…
Singularities of bi-Hamiltonian systems
Alexey Bolsinov, Anton Izosimov
We study the relationship between singularities of bi-Hamiltonian systems and algebraic properties of compatible Poisson brackets. As the main tool, we introduce the notion of line…
A note on relative equilibria of multidimensional rigid body
Anton Izosimov
It is well known that a rotation of a free generic three-dimensional rigid body is stationary if and only if it is a rotation around one of three principal axes of inertia. As it w…
The derived algebra of a stabilizer, families of coadjoint orbits, and sheets
Anton Izosimov
Let be a finite-dimensional real or complex Lie algebra, and let . In the first part of the paper, the relation is discussed between the deriv…