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...e also polynomials of the second and fourth degrees. Remind that description of all the natural Hamiltonian systems on closed surfaces admitting integrals polynomial in momenta is a classical problem =-=[1]-=-. For the systems with polynomial in momenta integrals of degree one or two there exists a complete description and classification [2]. i=1 1The Kowalevski top is an example of a conservative system ...

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... admitting integrals polynomial in momenta is a classical problem [1]. For the systems with polynomial in momenta integrals of degree one or two there exists a complete description and classification =-=[2]-=-. i=1 1The Kowalevski top is an example of a conservative system on S 2 which possesses an integral of degree four in momenta [3]. Later Goryachev [4] and Chaplygin [5] found generalization of the Ko...

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...xtended in [6]. The main aim of this note is to consider some another generalization of the Kowalevski-Goryachev-Chaplygin system using the reflection equation theory [7]. 2 Generic case Following to =-=[8]-=- let us consider Lax matrix for the generalized Lagrange system ( A B T(λ) = B∗ ) (λ) D with the following entries polynomial in the spectral parameter λ A(λ) = λ 2 ( − 2λαJ3 + α 2 ) − f(x3) J 2 3 − J...