Geodesic
Third Order ODEs Systems and Its Characteristic Connections
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2011_7_a75,
     author = {Alexandr Medvedev},
     title = {Third {Order} {ODEs} {Systems} and {Its} {Characteristic} {Connections}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2011},
     volume = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a75/}
}
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Alexandr Medvedev. Third Order ODEs Systems and Its Characteristic Connections. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a75/

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