Abstract
For any given vector field X defined on some open set M ⊂∝2, we characterize the prolongations X *n of X to the nth jet space M (n), n≥1, such that a complete system of invariants for X *n can be obtained by derivation of lower-order invariants. This leads to characterizations of C ∞-symmetries and to new procedures for reducing the order of an ordinary differential equation.
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Muriel, C., Romero, J.L. Prolongations of Vector Fields and the Invariants-by-Derivation Property. Theoretical and Mathematical Physics 133, 1565–1575 (2002). https://doi.org/10.1023/A:1021107112966
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DOI: https://doi.org/10.1023/A:1021107112966