  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.
