Symmetry gaps for higher order ordinary differential equations

Published 8 Oct 2021 in math.DG | (2110.03954v2)

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.

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