ИСТИНА

The full symmetric Toda system is determined by the Cartan decompo- sition of a real Lie algebra. It can can be described with the help of gradient a dynamic system on the flag space of the corresponding Lie group. In my talk I will describe the invariant surfaces of this system, associated with the representations of the Lie algebra. In many situations these surfaces allows one describe the phase portrait of the system in the terms of Bruhat order of the corresponding (relative) Weyl group.