### Geometry of second-order connections and ordinary differential equations

Alexandr Vondra (1995)

Mathematica Bohemica

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The geometry of second-order systems of ordinary differential equations represented by $2$-connections on the trivial bundle $error\mathbb{R}\times M\to \mathbb{R}$ is studied. The formalism used, being completely utilizable within the framework of more general situations (partial equations), turns out to be of interest in confrontation with a traditional approach (semisprays), moreover, it amounts to certain new ideas and results. The paper is aimed at discussion on the interrelations between all types of connections having...