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The structure of the Euler-Lagrange mapping

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Abstract

The purpose of this paper is to review properties of the Euler-Lagrange mapping in the higher order variational theory on fibred manifolds. We present basic theorems on the kernel of the Euler-Lagrange mapping, describing variationally trivial Lagrangians, and its image, characterizing variational source forms. We discuss invariance properties of Lagrangians and Euler-Lagrange forms, and the Noether’s theory.

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Correspondence to D. Krupka.

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Krupka, D. The structure of the Euler-Lagrange mapping. Russ Math. 51, 52–70 (2007). https://doi.org/10.3103/S1066369X07120043

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