Rationality of the Poincaré series in Arnold’s local problems of analysis. (English. Russian original) Zbl 1205.53013

Sarkisyan, R. A.

Izv. Math. 74, No. 2, 411-438 (2010); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 74, No. 2, 195-224 (2010).

For any smooth action of a Lie pseudo-group, the author constructs a domain (in the corresponding infinite jet space) consisting of finitely many open sets (atoms) such that all points in each atom have the same rational Poincaré series. It is also proved that these series can be calculated algorithmically.

Reviewer: Miroslav Doupovec (Brno)

MSC:

53A55	Differential invariants (local theory), geometric objects
58A20	Jets in global analysis

Keywords:

orbits of actions of diffeomorphism groups; jet spaces; dimensions of orbits; Poincaré series