1 - 10 of 13 articles
A Hamiltonian system on a Poisson manifold M is called integrable if it possesses sufficiently many commuting first integrals f
1, … f
which are functionally independent on M almost everywhere. We study the structure of the singular set K where the differentials df
1, …, df
We consider several well-known isomorphisms between Jacobi’s geodesic problem and some integrable cases from rigid body dynamics (the cases of Clebsch and Brun). A relationship between these isomorphisms is indicated. The problem of compactification for geodesic flows on noncompact surfaces is...
A class of elliptic curves with associated Lax matrices is considered. A family of dynamical systems on e(3) parametrized by polynomial a with the above Lax matrices are constructed. Five cases from the family are selected by the condition of preserving the standard measure. Three of them are...
A detailed description of topology of integrable billiard systems is given. For elliptical billiards and geodesic billiards on ellipsoid, the corresponding Fomenko graphs are constructed.
We revise the solution to the problem of Hamiltonization of the n-dimensional Veselova nonholonomic system studied previously in . Namely, we give a short and direct proof of the hamiltonization theorem and also show the trajectorial equivalence of the problem with the geodesic flow on the...
We consider the class of ellipsoidal gas clouds expanding into a vacuum [1, 2] which has been shown to be a Liouville integrable Hamiltonian system . This system presents several interesting features, such as the Painlevé property [4, 5], the existence of Bäcklund transformations and the...
We apply a non-linear matrix transformation of Lie-Bäcklund type on a seed soliton configuration in order to obtain a new solitonic solution in the framework of the 5D low-energy effective field theory of the bosonic string. The seed solution represents a stationary axisymmetric two-soliton...
The Poincaré model for dynamics of a collisionless gas in a rectangular parallelepiped with mirror walls is considered. The question on smoothing of the density and the temperature of this gas and conditions for the monotone growth of the coarse-grained entropy are discussed. All these effects...
We discuss some special classes of canonical transformations of the time variable, which relate different integrable systems. Such dual systems have different integrals of motion, Lax equations, separated variables and bi-hamiltonian structures. As an example the two-dimensional periodic Toda...
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