Related papers: Separation of variables in the generalized 4th App…
In the phase space of the integrable Hamiltonian system with three degrees of freedom used to describe the motion of a Kowalevski-type top in a double constant force field, we point out the four-dimensional invariant manifold. It is shown…
The article continues the author's publication in [Mech. Tverd. Tela, No. 35, 2005 and No. 38, 2008], in which we investigate the integrable dynamical system induced on one four-dimensional submanifold of the phase space of the problem of a…
The article continues the author's publication in [Mech. Tverd. Tela, No. 34, 2004], in which the generalizations of the Appelrot classes of the Kowalevski top motions are found for the case of the double force field. We consider the…
In the problem of motion of the Kowalevski top in a double force field the 4-dimensional invariant submanifold of the phase space was pointed out by M.P.Kharlamov (Mekh. Tverd. Tela, 32, 2002). We show that the equations of motion on this…
The Kowalevski top in two constant fields is known as the unique profound example of an integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions. As the first approach to…
For the integrable system on $e(3,2)$ found by Sokolov and Tsiganov we obtain explicit equations of some invariant 4-dimensional manifolds on which the induced systems are almost everywhere Hamiltonian with two degrees of freedom. These…
The complete variables separation is given for one Hamiltonian system with two degrees of freedom arising in the motion of the Kowalevski type top in two constant fields.
For the system with two degrees of freedom, which is an analogue of the 4th Appelrot class for a gyrostat of the Kowalevski type in a double force field the problem of the classification of bifurcation diagrams is solved. The separating set…
We consider the integrable system with three degrees of freedom for which Sokolov and Tsiganov specified Lax representation. Lax representation generalizes L-A pair of the Kowalevski gyrostat in two constant fields, found by A.G.Reyman and…
The case of motion of a generalized two-field gyrostat found by V.V.Sokolov and A.V.Tsiganov is known as a Liouville integrable Hamiltonian system with three degrees of freedom. We find a set of points at which the momentum map has rank 1.…
Consider a rigid body having a fixed point in a superposition of two constant force fields (for example, gravitational and magnetic). Introducing the condition of Kowalevski type, O.I.Bogoyavlensky (1984) has found the first integral…
Phase ordering dynamics of the (2+1)- and (3+1)-dimensional $\phi^4$ theory with Hamiltonian equations of motion is investigated numerically. Dynamic scaling is confirmed. The dynamic exponent $z$ is different from that of the Ising model…
The geometric approach for Painlev\'e and quasi-Painlev\'e differential equations in the complex plane is applied to non-autonomous Hamiltonian systems, quartic in the dependent variables. By computing their defining manifolds (analogue of…
In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map of Weingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type…
It is shown that the $F_4$ rational and trigonometric integrable systems are exactly-solvable for {\it arbitrary} values of the coupling constants. Their spectra are found explicitly while eigenfunctions by pure algebraic means. For both…
We consider spacelike surfaces in the four-dimensional Minkowski space and introduce geometrically an invariant linear map of Weingarten-type in the tangent plane at any point of the surface under consideration. This allows us to introduce…
The Kowalevski gyrostat in two constant fields is known as the unique example of an integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions and still having the clear mechanical…
In the paper, we consider a completely integrable Hamiltonian system with three degrees of freedom found by V.V.Sokolov and A.V.Tsiganov. This system is known as the generalized two-field gyrostat. For the case of only gyroscopic forces…
In the paper we consider several dynamical systems that admit a separation of variables on the algebraic curve of genus 4. The main result of the paper is an explicit formula for the action of these systems. We find it directly from the…
Separation of variables by means of the orbit method is implemented to integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra. This is a development and a kind of explanation for Sklyanin's procedure of separation of…