On bi-hamiltonian structure of some integrable systems on so*(4)

Abstract

We classify all the quadratic Poisson structures on $s{o}^{\ast }(4)$ and $e^{\ast }(3)$, which have the same foliation by symplectic leaves as the canonical Lie-Poisson tensors. The separated variables for the some of the corresponding bi-integrable systems are constructed.

LaTeX with Amsfonts, 13 pages, corrected typos

References in corpus (3)

• A family of the Poisson brackets compatible with the Sklyanin bracket
• The Poisson bracket compatible with the classical reflection equation algebra
• On the Darboux-Nijenhuis Variables for the Open Toda Lattice

Cited by in corpus (10)

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• On the generalized integrable Chaplygin system
• On bi-integrable natural Hamiltonian systems on the Riemannian manifolds
• On bi-hamiltonian geometry of the Lagrange top
• Hamiltonization and separation of variables for Chaplygin ball on a rotating plane
• New Variables of Separation for the Steklov-Lyapunov System
• Integrable Systems Related to Deformed $\mathfrak{so}(5)$
• On the bi-Hamiltonian structure of Bogoyavlensky system on $so(4)$
• On bi-Hamiltonian structure of some superintegrable systems