Rationality of the Poincaré series in Arnold's local problems of analysis

Poincaré Function for Moduli of Differential-Geometric Structures

“…This fact was experimentally observed by V. Arnold for some local problems in analysis and geometry [1]. Later this conjecture was proved for the diffeomorphism pseudogroups acting on natural geometric bundles in [33], and then for general algebraic pseudogroups acting on algebraic differential equations in [23]. The basic assumption in the last reference, in addition to algebraicity, is transitivity of the pseudogroup action on the base manifold, and we adapt this also in what follows.…”