Geodesic
A~category-theoretic approach extending the notion of connection in a~natural way, and its application to the geometry of differential systems
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 55-63.

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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; O. M. Omelyan. A~category-theoretic approach extending the notion of connection in a~natural way, and its application to the geometry of differential systems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 1, pp. 55-63. http://geodesic.mathdoc.fr/item/FPM_2010_16_1_a4/

[1] Evtushik L. E., “Neevklidovy geometrii na osnove obyknovennykh differentsialnykh sistem vysshikh poryadkov”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 1994, no. 2, 86–98 | MR | Zbl