Symmetry gaps for higher order ordinary differential equations

Abstract

The maximal contact symmetry dimensions for scalar ODEs of order $\ge 4$ and vector ODEs of order $\ge 3$ are well known. Using a Cartan-geometric approach, we determine for these ODEs the next largest realizable (submaximal) symmetry dimension. Moreover, finer curvature-constrained submaximal symmetry dimensions are also classified.

18 pages, 2 figures

References in corpus (4)

• On automorphism groups of some types of generic distributions
• Third Order ODEs Systems and Its Characteristic Connections
• On canonical Cartan connections associated to filtered G-structures
• Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations

Cited by in corpus (2)

• Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations
• On Uniqueness of Submaximally Symmetric Vector Ordinary Differential Equations of C-Class