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This article is cited in 3 scientific papers (total in 3 papers)
Regularity and Tresse's theorem for geometric structures
R. A. Sarkisyan, I. G. Shandra Finance Academy under the Government of the Russian Federation
Abstract:
For any non-special bundle $P\to X$ of geometric structures we prove
that the $k$-jet space $J^k$ of this bundle with an appropriate $k$
contains an open dense domain $U_k$ on which Tresse's theorem holds.
For every $s\geq k$ we prove that the pre-image $\pi^{-1}(k,s)(U_k)$ of $U_k$
under the natural projection $\pi(k,s)\colon J^s\to J^k$ consists
of regular points. (A point of $J^s$ is said to be regular if the orbits
of the group of diffeomorphisms induced from $X$ have locally constant
dimension in a neighbourhood of this point.)
DOI:
https://doi.org/10.4213/im1049
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English version:
Izvestiya: Mathematics, 2008, 72:2, 345–382
Bibliographic databases:
UDC:
514.763
MSC: 53A55 Received: 10.04.2006
Citation:
R. A. Sarkisyan, I. G. Shandra, “Regularity and Tresse's theorem for geometric structures”, Izv. RAN. Ser. Mat., 72:2 (2008), 151–192; Izv. Math., 72:2 (2008), 345–382
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http://mi.mathnet.ru/eng/izv1049https://doi.org/10.4213/im1049 http://mi.mathnet.ru/eng/izv/v72/i2/p151
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This publication is cited in the following articles:
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Kruglikov B., “Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond”, Differential Equations: Geometry, Symmetries and Integrability - the Abel Symposium 2008, Abel Symposia, 5, 2009, 199–221
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R. A. Sarkisyan, “Rationality of the Poincaré series in Arnold's local problems of analysis”, Izv. Math., 74:2 (2010), 411–438
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Kruglikov B., Lychagin V., “Global Lie–Tresse theorem”, Sel. Math.-New Ser., 22:3 (2016), 1357–1411
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