Third Order ODEs Systems and Its Characteristic Connections

Details Third Order ODEs Systems and Its Characteristic Connections Third Order ODEs Systems and Its Characteristic Connections

2011-04-05

arxiv.org/abs/1104.0965v5

SIGMA 7 (2011), 076, 15 pages

Mathematics

Differential Geometry

Scientific paper

10.3842/SIGMA.2011.076

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.

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