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**Higher-order differential equations represented by connections on prolongations of a fibered manifold.**
*(English)*
Zbl 0992.34006

Here, the author continues his studies on the geometry of ordinary differential equations extending his previous ideas, constructions and results from the first- and second-order situation to that of an arbitrary finite-order one. The main subjects are: jet prolongations of sections and morphisms, total derivatives, prolongations of vector fields, the contact structure and the Cartan distribution, repeated jets, \((k+1)\)-connections on fibered manifolds, higher-order equations represented by connections, prolongations and fields of paths, symmetries and vertical prolongations, connections on affine bundle \(J^{k+1}\pi \rightarrow J^k \pi\) for \(\pi :Y \rightarrow X\) an arbitrary fibered bundle, the method of characteristics, the method of fields of paths, strong horizontal distributions, semispray connections, time-dependent higher-order differential equations. The notions are clearly explained and the proofs are given in all details. Several examples are included.

Reviewer: M.Anastasiei (Iaşi)