This article is cited in 2 papers

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

R. A. Sarkisyan

Finance Academy under the Government of the Russian Federation

Abstract: 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, dimensions of orbits, Poincaré series of dimensions of orbits, rationality of a series.

UDC: 512.628.2

MSC: 53A55, 58A20

Received: 11.10.2007
Revised: 09.06.2008

DOI: 10.4213/im2735

 English version: Izvestiya: Mathematics, 2010, 74:2, 411–438

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