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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 076, 15 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.076 (Mi sigma634) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Third Order ODEs Systems and Its Characteristic Connections

Alexandr Medvedev

Faculty of Applied Mathematics, Belarusian State University, 4, Nezavisimosti Ave., 220030, Minsk, Republic of Belarus
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DOI: https://doi.org/10.3842/SIGMA.2011.076
Abstract: We compute the characteristic Cartan connection associated with a system of third order ODEs. Our connection is different from Tanaka normal one, but still is uniquely associated with the system of third order ODEs. This allows us to find all fundamental invariants of a system of third order ODEs and, in particular, determine when a system of third order ODEs is trivializable. As application differential invariants of equations on circles in $\mathbb R^n$ are computed.
Keywords: geometry of ordinary differential equations; normal Cartan connections.
Received: April 20, 2011; in final form July 27, 2011; Published online August 3, 2011
Bibliographic databases:
Document Type: Article
MSC: 34A26; 53B15
Language: English
Citation: Alexandr Medvedev, “Third Order ODEs Systems and Its Characteristic Connections”, SIGMA, 7 (2011), 076, 15 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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