We consider integrable system on the sphere S 2 with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system. 1

-field Kowalewski gyrostat and the so(p,q) Kowalewski top are found. All our Lax pairs are deformations of the corresponding Lax representations found by Reyman and Semenov-Tian Shansky. In addition, a similar deformation of the Goryachev-Chaplygin top and its 3 × 3 matrix Lax representation is constructed. 1

Based on the RTT relation for the given rational R-matrix the Yangian and truncated Yangian are discussed. The former can be used to generate the longrange interaction models, whereas the latter can be related to the Goryachev-Chaplygin(GC) gyrostat. The trigonometric extension of the Goryachev-Chaplygin

of variables for them. The models obtained are deformations of known integrable systems like the Goryachev-Chaplygin top, the Toda lattice and the Heisenberg model. 1 Introduction.

) containing as special cases examples dueto Goryachev, Chaplygin, Dullin, Matveev and Tsiganov. Integrable systems 1 1

, and therefore is a Hamiltonian vector field. As examples we treat the Goryachev-Chaplygin top, the Toda lattice and the Calogero-Moser system, and construct their global Hamiltonians. We show that the simplest choice of Hamiltonian leads to the Toda lattice. 1

is a Hamiltonian vector field. As examples we treat the Goryachev-Chaplygin top, the Toda lattice and the Calogero-Moser system, and construct their global Hamiltonians. We show that the simplest choice of Hamiltonian leads to the Toda lattice. 1 Introduction Simple questions about the existence

Generalizations of the Kovalevskaya, Chaplygin, Goryachev–Chaplygin and Bogoyavlensky systems on a bundle are considered in this paper. Moreover, a method of introduction of separating variables and action–angle variables is described. Another integration method for the Kovalevskaya top

, the discrete self-trapping model and the Goryachev-Chaplygin gyrostat. 1 Introduction. The ingenious discovery of Magri [6, 7] that integrable Hamiltonian systems usually prove to be bi-Hamiltonian, and vice versa, leads us to the following fundamental problem: given a dynamical system which is Hamiltonian

(ν, ω). (3) Of special interest are the general integrability cases: the solutions of Lagrange, Euler, Kovalevskaya, and Goryachev-Chaplygin. The first two can be included in Smale’s scheme for studying the phase topology of natural systems [4]; their analysis is carried out in [5]. The topology