Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 076, 15 pages      arXiv:1104.0965      https://doi.org/10.3842/SIGMA.2011.076

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

Received April 20, 2011, in final form July 27, 2011; Published online August 03, 2011

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 Rn are computed.

Key words: geometry of ordinary differential equations; normal Cartan connections.

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