Abstract: We will discuss the following statements: The algebra of differential invariants of an algebraic transitive pseudogroup action on a differential equation is generated by a finite number of polynomial-rational differential invariants and invariant derivations. The set of singularities is contained in a space of finite positive codimension in the infinitely prolonged equation (in un-constrained case: in the space of infinite jets). In a complement of a space of infinite codimension the Poincare series is a rational function. We will also consider several applications.
The talk is based on a joint work with V. Lychagin