ИСТИНА

This talk is devoted to the Lie-Bianchi integrability of the full symmetric Toda system, i.e. to the fact that there exists a solvable Lie algebra of vector fields of dimension on the phase space of this system such that the system is invariant with respect to the action of these fields. The proof is based on the use of symmetries of the full sym metric system, which we described earlier in [1], and the appearance of the structure of the stochastic Lie algebra in their description. The talk is based on the joint work with Yu. Chernyakov and G. Sharygin arXiv:2506.07113. REFERENCES 1. A. S. Sorin, Yu. B. Chernyakov, G. I. Sharygin, Vector fields and invariants of the full symmetric Toda system, Theoret. and Math. Phys., 216:2, 1142 1157 (2023).