Two-dimensional systems that arise from the Noether classification of Lagrangians on the line
The paper under review is devoted to a Noether classification for systems of two second-order ODEs of variational type that arise from the submaximal and maximal Noether symmetry classification of Lagrangians on the line. A main tool is the notion of \textit{Noether-like operators} which provides an algebraic study of such systems derived from complex Euler-Lagrange equations and also yield new first integrals. The main results are: 1) a classification of systems with respect to the Noether-like operators they admit; 2) a Noether counting theorem as an analogue of Lie counting theorem.
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