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We compute the characteristic Cartan connection associated with a system ofthird order ODEs. Our connection is different from Tanaka normal one, but stillis uniquely associated with the system of third order ODEs. This allows us tofind all fundamental invariants of a system of third order ODEs and, inparticular, determine when a system of third order ODEs is trivializable. Asapplication differential invariants of equations on circles in ${\mathbb R}^n$are computed.

Third Order ODEs Systems and Its Characteristic Connections