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Sibirskii Matematicheskii Zhurnal, 2009, Volume 50, Number 1, Pages 47–62 (Mi smj1936)  
This article is cited in 8 scientific papers (total in 8 papers)

Applications of the group analysis of differential equations to some systems of noncommuting $C^1$-smooth vector fields

A. V. Greshnov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (361 kB) Citations (8)
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Abstract: Given a canonical basis of $C^1$-smooth vector fields $\{\widetilde X_i\}$ satisfying certain restrictions on commutators, we prove an existence theorem for their local nilpotent homogeneous approximation at the origin using the methods of the group analysis of differential equations. We study the properties of the quasimetrics induced by some systems of vector fields related to $\{\widetilde X_i\}$.
Keywords: vector field, Arzelà–Ascoli theorem, theorem on the existence and uniqueness for ODEs, commutator, quasimetric.
Received: 15.03.2007
Revised: 29.08.2008
English version:
Siberian Mathematical Journal, 2009, Volume 50, Issue 1, Pages 37–48
DOI: https://doi.org/10.1007/s11202-009-0005-8
Bibliographic databases:
UDC: 514.763+512.812.4+517.911
Language: Russian
Citation: A. V. Greshnov, “Applications of the group analysis of differential equations to some systems of noncommuting $C^1$-smooth vector fields”, Sibirsk. Mat. Zh., 50:1 (2009), 47–62; Siberian Math. J., 50:1 (2009), 37–48
Citation in format AMSBIB
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\paper Applications of the group analysis of differential equations to some systems of noncommuting $C^1$-smooth vector fields
\jour Sibirsk. Mat. Zh.
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\issue 1
\pages 47--62
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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