Abstract
We give the widest geometrical generalization of the notion of connection in fiber spaces that allows one to adequately construct the geometry of ordinary differential systems of any order. In this area, there is a theory of nonlinear stable connections developed by the first author. Here we apply it to fourth-order systems.
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L. E. Evtushik, “Non-Euclidean geometries on the basis of higher-order ordinary differential systems,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 2, 86–98 (1994).
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 1, pp. 55–63, 2010.
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Evtushik, L.E., Omelyan, O.M. A category-theoretic approach extending the notion of connection in a natural way, and its application to the geometry of differential systems. J Math Sci 177, 551–557 (2011). https://doi.org/10.1007/s10958-011-0480-x
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DOI: https://doi.org/10.1007/s10958-011-0480-x