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This article is cited in 2 scientific papers (total 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.
DOI:
https://doi.org/10.4213/im2735
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English version:
Izvestiya: Mathematics, 2010, 74:2, 411–438
Bibliographic databases:
UDC:
512.628.2
MSC: 53A55, 58A20 Received: 11.10.2007 Revised: 09.06.2008
Citation:
R. A. Sarkisyan, “Rationality of the Poincaré series in Arnold's local problems of analysis”, Izv. RAN. Ser. Mat., 74:2 (2010), 195–224; Izv. Math., 74:2 (2010), 411–438
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Linking options:
http://mi.mathnet.ru/eng/izv2735https://doi.org/10.4213/im2735 http://mi.mathnet.ru/eng/izv/v74/i2/p195
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This publication is cited in the following articles:
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Kruglikov B. Lychagin V., “Global Lie–Tresse theorem”, Sel. Math.-New Ser., 22:3 (2016), 1357–1411
-
Boris Kruglikov, “Poincaré function for moduli of differential-geometric structures”, Mosc. Math. J., 19:4 (2019), 761–788
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