Third Order ODEs Systems and Its Characteristic Connections

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 ${\mathbb{R}}^n$ are computed.

Cited by in corpus (7)

• Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations
• Symmetry gaps for higher order ordinary differential equations
• On C-class equations
• On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class
• On the geometry of conformal geodesics equations
• Parabolic quasi-contact cone structures with an infinitesimal symmetry
• Fundamental invariants of systems of ODEs of higher order