54 citations · 777 across the 87 of their papers we have counts for
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Canonical transformations of the time for the Toda lattice and the Holt system
Andrey Tsiganov
For the Toda lattice and the Holt system we consider properties of canonical transformations of the extended phase space, which preserve integrability. The separated variables are…
Canonical transformations of the extended phase space, Toda lattices and Stackel family of integrable systems
Andrey Tsiganov
We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other compl…
On integrable deformations of the spherical top
Andrey Tsiganov
The motion on the sphere with the potential is considered. The Lax representation and the linearisation procedure for this two-dimensional integrable…
The Lax pairs for the Holt system
A. V. Tsiganov
By using non-canonical transformation between the Holt system and the Henon-Heiles system the Lax pairs for all the integrable cases of the Holt system are constructed from the kno…
Duality between integrable Stackel systems
Andrey Tsiganov
For the Stackel family of the integrable systems a non-canonical transformation of the time variable is considered. This transformation may be associated to the ambiguity of the Ab…
Dynamical boundary conditions for integrable lattices
Andrey Tsiganov
Some special solutions to the reflection equation are considered. These boundary matrices are defined on the common quantum space with the other operators in the chain. The relatio…
The Stackel systems and algebraic curves
A. V. Tsiganov
We show how the Abel-Jacobi map provides all the principal properties of an ample family of integrable mechanical systems associated to hyperelliptic curves. We prove that derivati…
On superintegrable systems closed to geodesic motion
A. V. Tsiganov
In this work we consider superintegrable systems in the classical -matrix method. By using other authomorphisms of the loop algebras we construct new superintegrable systems wit…
Automorphisms of sl(2) and dynamical r-matrices
A. V. Tsiganov
Two outer automorphisms of infinite-dimensional representations of algebra are considered. The similar constructions for the loop algebras and yangians are presented. The c…
The Kowalewski top: a new Lax representation
A. V. Tsiganov
The 2x2 monodromy matrices for the Kowalewski top on the Lie algebras e(3), so(4) and so(3,1) are presented. The corresponding quadratic R-matrix structure is the dynamical deforma…
Quasi-point separation of variables for the Henon-Heiles system and a system with quartic potential
S. Rauch-Wojciechowski, A. V. Tsiganov
We examine the problem of integrability of two-dimensional Hamiltonian systems by means of separation of variables. The systematic approach to construction of the special non-pure…