The gap phenomenon in the dimension study of finite type systems
  In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the symmetries of geometric structures and differential equations. A general result clarifying this effect in the case, when the structure is associated to a vector distribution, is proposed. 
Boris Kruglikov
math.DG math.CA