Symmetry gaps for higher order ordinary differential equations

The maximal contact symmetry dimensions for scalar ODEs of order >= 4 and vector ODEs of order >= 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. (c) 2022 The Author(s). Published by Elsevier Inc.

Automated summary

This article presents the maximal contact symmetry dimensions for scalar ODEs and vector ODEs, along with the determination of submaximal symmetry dimensions using a Cartan-geometric approach. It also provides a classification of finer curvature-constrained submaximal symmetry dimensions.