Invariant critical sets of conserved quantities
  For a dynamical system we will construct various invariant sets starting from its conserved quantities. We will give conditions under which certain solutions of a nonlinear system are also solutions for a simpler dynamical system, for example when they are solutions for a linear dynamical system. We will apply these results to the example of Toda lattice. 
Petre Birtea and Dan Com\u{a}nescu
math.DS