Geodesic
Rationality of the Poincaré series in Arnold's local problems of analysis
Izvestiya. Mathematics, Tome 74 (2010) no. 2, pp. 411-438

Voir la notice de l'article provenant de la source Math-Net.Ru

For any smooth action of a Lie pseudo-group we construct 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. We also prove that these series can be calculated algorithmically.
Keywords: orbits of actions of diffeomorphism groups in jet spaces, rationality of a series.
Mots-clés : dimensions of orbits, Poincaré series of dimensions of orbits 
R. A. Sarkisyan. Rationality of the Poincaré series in Arnold's local problems of analysis. Izvestiya. Mathematics, Tome 74 (2010) no. 2, pp. 411-438. http://geodesic.mathdoc.fr/item/IM2_2010_74_2_a6/
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