This article is cited 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

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.

MSC: 34A26; 53B15

Received: April 20, 2011; in final form July 27, 2011; Published online August 3, 2011

Language: English

DOI: 10.3842/SIGMA.2011.076

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ArXiv: 1104.0965