I. Kozlov

collaborators

5 papers

math.SG2024

Local bi-integrability of bi-Hamiltonian systems, Part II: Real smooth case

I. K. Kozlov

We prove that any bi-Hamiltonian system $v = (A + λ B) d H_{λ}$ on a real smooth manifold that is Hamiltonian with respect all Poisson brackets $\left(\ma…

math.SG2024

Local bi-integrability of bi-Hamiltonian systems via bi-Poisson reduction

I. K. Kozlov

We prove that any bi-Hamiltonian system $v = (A + λ B) d H_{λ}$ that is Hamiltonian with respect all Poisson brackets $A + λ B$ is loca…

math.SG2024

Integrability of bi-Hamiltonian systems using Casimir functions and characteristic polynomials

I. K. Kozlov

In this paper we prove that for a pencil of compatible Poisson brackets $P = {A + λ B}$ the local Casimir functions of Poisson brackets $…

math.RA2024

Geometry of bi-Lagrangian Grassmannian

I. K. Kozlov

This paper explores the structure of bi-Lagrangian Grassmanians for pencils of $2$ -forms on real or complex vector spaces. We reduce the analysis to the pencils whose Jordan-Kronec…

math.DG2022

Invariant foliations of non-degenerate bi-Hamiltonian structures

Ivan Kozlov

In this paper, we describe all invariant distributions of non-degenerate bi-Hamiltonian structures and investigate their integrability in the neighbourhood of a generic point.