Flessas, G. R.; Govinder, K. S.; Leach, P. G. L. Remarks on the symmetry Lie algebras of first integrals of scalar third-order ordinary differential equations with maximal symmetry. (English) Zbl 0919.34009 Bull. Greek Math. Soc. 36, 63-79 (1994). Summary: The authors present first integrals of third-order ordinary differential equations with maximal symmetry by considering Lie symmetries of the equations. Properties of these integrals and algebras of their symmetries are discussed and a connection to higher-order equations and maximal symmetry is pursued. Second-order and third-order equations with maximal symmetry are shown to be anomalies in the group theoretic approach to understanding \(n\)th-order equations with maximal symmetry and their first integrals. Cited in 6 Documents MSC: 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 17B66 Lie algebras of vector fields and related (super) algebras 37C80 Symmetries, equivariant dynamical systems (MSC2010) Keywords:first integrals; third-order ordinary differential equations; maximal symmetry; Lie symmetries PDFBibTeX XMLCite \textit{G. R. Flessas} et al., Bull. Greek Math. Soc. 36, 63--79 (1994; Zbl 0919.34009) Full Text: EuDML