This article is cited in 28 papers

Prolongations of Vector Fields and the Invariants-by-Derivation Property

C. Muriel, J. L. Romero

Universidad de Cadiz

Abstract: For any given vector field $X$ defined on some open set $M\subset \mathbb R^2$, we characterize the prolongations $X^*_n$ of $X$ to the nth jet space $M^{(n)}$, $n\geq 1$, such that a complete system of invariants for $X^*_n$ can be obtained by derivation of lower-order invariants. This leads to characterizations of $C^{\infty }$-symmetries and to new procedures for reducing the order of an ordinary differential equation.

Keywords: $C^{\infty }$-symmetry, differential invariants, reductions of ordinary differential equations.

DOI: 10.4213/tmf398

 English version: Theoretical and Mathematical Physics, 2002, 133:2, 1565–1575

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