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

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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, Poincaré series of dimensions of orbits, rationality of a series.
Mots-clés : dimensions of orbits 
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     author = {R. A. Sarkisyan},
     title = {Rationality of the {Poincar\'e} series in {Arnold's} local problems of analysis},
     journal = {Izvestiya. Mathematics },
     pages = {411--438},
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     volume = {74},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2010_74_2_a6/}
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R. A. Sarkisyan. Rationality of the Poincar\'e 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/