17 citations · 43 across the 13 of their papers we have counts for
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The Lie -Bianchi integrability of the full symmetric Toda system
Yury B. Chernyakov, Georgy I. Sharygin, Dmitry V. Talalaev
In this paper we prove that the full symmetric Toda system is integrable in the sense of the Lie-Bianchi criterion, i.e. that there exists a solvable Lie algebra of vector fields o…
Full symmetric Toda system and vector fields on the group
Yu. B. Chernyakov, G. I. Sharygin
In this paper we discuss the relation between the functions that give first integrals of full symmetric Toda system (an important Hamilton system on the space of traceless real sym…
Full symmetric Toda system: QR-solution for complete DLNT-family
Yury B. Chernyakov, Georgy I. Sharygin, Dmitry V. Talalaev
The paper is devoted to the algebraic and geometric aspects of the full symmetric Toda system. We construct a solution to the complete Deift-Li-Nanda-Tomei flows system using the Q…
On the invariants of the full symmetric Toda system
Yu. B. Chernyakov, G. I Sharygin, A. S. Sorin
In this paper we continue our study of the geometric properties of full symmetric Toda systems from \cite{CSS14,CSS17,CSS19}. Namely we describe here a simple geometric constructio…
Phase portraits of the generalized full symmetric Toda systems on rank 2 groups
Yu. B. Chernyakov, G. I Sharygin, A. S. Sorin
In this paper we continue investigations that we began in our previous works, where we proved, that the phase diagram of Toda system on special linear groups can be identified with…
Bruhat Order in the Full Symmetric Toda Lattice on Partial Flag Space
Yury B. Chernyakov, Georgy I. Sharygin, Alexander S. Sorin
In our previous paper [Comm. Math. Phys. 330 (2014), 367-399] we described the asymptotic behaviour of trajectories of the full symmetric Toda lattice in the case…
Bruhat Order in Full Symmetric Toda System
Yu. B. Chernyakov, G. I. Sharygin, A. S. Sorin
In this paper we discuss some geometrical and topological properties of the full symmetric Toda system. We show by a direct inspection that the phase transition diagram for the ful…