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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 270, Pages 147–160 (Mi tm3023)  
This article is cited in 2 scientific papers (total in 2 papers)

Families of vector fields which generate the group of diffeomorphisms

Marco Caponigroab

a Institut Èlie Cartan de Nancy UMR 7502, Nancy-Université, CNRS, INRIA, Nancy cedex, France
b SISSA, Trieste, Italy
Full-text PDF (223 kB) Citations (2)
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Abstract: Given a compact manifold $M$ and a family of vector fields $\mathcal F$ such that the group generated by $\mathcal F$ acts transitively on $M$, we prove that the group of all diffeomorphisms of $M$ that are isotopic to the identity is generated by the exponentials of vector fields in $\mathcal F$ rescaled by smooth functions.
Received in March 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 270, Pages 141–155
DOI: https://doi.org/10.1134/S0081543810030107
Bibliographic databases:
Document Type: Article
UDC: 517.97
Language: English
Citation: Marco Caponigro, “Families of vector fields which generate the group of diffeomorphisms”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 270, MAIK Nauka/Interperiodica, Moscow, 2010, 147–160; Proc. Steklov Inst. Math., 270 (2010), 141–155
Citation in format AMSBIB
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\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 2 articles:
    1. A. Scagliotti, S. Farinelli, “Normalizing flows as approximations of optimal transport maps via linear-control neural ODEs”, Nonlinear Analysis, 257 (2025), 113811  crossref
    2. Marco Caponigro, “Orientation preserving diffeomorphisms and flows of control-affine systems”, IFAC Proceedings Volumes, 44:1 (2011), 8016  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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