Contact symmetries and integrable non-linear dynamical systems

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Abstract
The authors present a systematic method of classifying and constructing invariants for Lagrangians containing arbitrary polynomial non-linear potentials. It is based on the assumption that these Lagrangians are invariant under contact groups of transformations. For a finite number of degrees of freedom they can prove integrability for a large class of polynomial potentials. The method can be extended in several directions.

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