On the bi-Hamiltonian structure of Bogoyavlensky system on $so(4)$

Abstract

We discuss bi-Hamiltonian structure for the Bogoyavlensky system on $so(4)$ with an additional integral of fourth order in momenta. An explicit procedure to find the variables of separation and the separation relations is considered in detail.

References in corpus (3)

• New variables of separation for particular case of the Kowalevski top
• On the generalized integrable Chaplygin system
• On bi-hamiltonian geometry of the Lagrange top