Zobrazeno 1 - 10
of 189
pro vyhledávání: '"Kozlov, A. K."'
Autor:
Kozlov, I. K.
We prove that any bi-Hamiltonian system $v = \left(\mathcal{A} + \lambda \mathcal{B}\right)dH_{\lambda}$ on a real smooth manifold that is Hamiltonian with respect all Poisson brackets $\left(\mathcal{A} + \lambda \mathcal{B}\right)$ is locally bi-in
Externí odkaz:
http://arxiv.org/abs/2410.21642
Autor:
Kozlov, I. K.
We prove that any bi-Hamiltonian system $v = \left(\mathcal{A} + \lambda \mathcal{B}\right)dH_{\lambda}$ that is Hamiltonian with respect all Poisson brackets $\mathcal{A} + \lambda \mathcal{B}$ is locally bi-integrable in both the real smooth case,
Externí odkaz:
http://arxiv.org/abs/2410.20574
Autor:
Kozlov, I. K.
In this paper we prove that for a pencil of compatible Poisson brackets $\mathcal{P} = \left\{\mathcal{A} + \lambda\mathcal{B} \right\}$ the local Casimir functions of Poisson brackets $\mathcal{A} + \lambda \mathcal{B}$ and coefficients of the chara
Externí odkaz:
http://arxiv.org/abs/2410.11032
Autor:
Kozlov, I. K.
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-Kronecker Canonical Form consists of Jordan blocks with the same eigenvalue.
Externí odkaz:
http://arxiv.org/abs/2409.09855
Autor:
Kozlov, I. K.
We introduce two novel techniques that simplify calculation of Jordan-Kronecker invariants for a Lie algebra $\mathfrak{g}$ and for a Lie algebra representation $\rho$. First, the stratification of matrix pencils under strict equivalence puts restric
Externí odkaz:
http://arxiv.org/abs/2409.09535
Autor:
Kozlov, I. K.
K. S. Vorushilov described Jordan-Kronecker invariants for semi-direct sums $\operatorname{sl} \ltimes \left(\mathbb{C}^n\right)^k$ if $k > n$ or if $n$ is a multiple of $k$. We describe the Jordan-Kronecker invariants in the cases $n \equiv \pm 1 \p
Externí odkaz:
http://arxiv.org/abs/2409.04454
Autor:
Kozlov, I. K.
We study commutative subalgebras in the symmetric algebra $S(\mathfrak{g})$ of a finite-dimensional Lie algebra $\mathfrak{g}$. A. M. Izosimov introduced extended Mischenko-Fomenko subalgebras $\tilde{\mathcal{F}}_a$ and gave a completeness criterion
Externí odkaz:
http://arxiv.org/abs/2307.10418
Autor:
Kozlov, I. K.
We study what Jordan-Kronecker invariants of Lie algebras, introduced by A. V. Bolsinov and P. Zhang, are possible. We completely solve this problem in the Jordan and the Kronecker cases. We prove that any JK invariants that contain the Kronecker $3
Externí odkaz:
http://arxiv.org/abs/2307.08642
Autor:
Kozlov, I. K., Oshemkov, A. A.
The paper presents an algorithm for topological classification of nondegenerate saddle-focus singularities of integrable Hamiltonian systems with three degrees of freedom up to semi-local equivalence. In particular, we prove that any singularity of s
Externí odkaz:
http://arxiv.org/abs/2301.10298
Autor:
Kozlov, I. K., Oshemkov, A. A.
Integrable systems with a linear periodic integral for the Lie algebra $\mathrm{e}(3)$ are considered. One investigates singulariries of the Liouville foliation, bifurcation diagram of the momentum mapping, transformations of Liouville tori, topology
Externí odkaz:
http://arxiv.org/abs/2301.05283