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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 2, Pages 195–224 (Mi izv2735)  
This article is cited in 1 scientific paper (total in 1 paper)

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

Full text: PDF file (686 kB)
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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

Citation in format AMSBIB
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  • https://doi.org/10.4213/im2735
  • http://mi.mathnet.ru/eng/izv/v74/i2/p195

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kruglikov B. Lychagin V., “Global Lie–Tresse theorem”, Sel. Math.-New Ser., 22:3 (2016), 1357–1411  crossref  mathscinet  zmath  isi  elib  scopus
    		• Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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