MATHEMATICA BOHEMICA, Vol. 120, No. 2, pp. 145-167, 1995

Geometry of second-order connections and ordinary differential equations

Alexandr Vondra

Department of Mathematics, Military Academy in Brno, PS 13, 612 00 Brno, Czech Republic

Abstract: The geometry of second-order systems of ordinary differential equations represented by $2$-connections on the trivial bundle $\operatorname{pr_1} \Bbb R\times M\to\Bbb R$ 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 to do with integral sections (geodesics), integrals and symmetries of the equations studied.

Keywords: connection, semispray, differential equation, integral, symmetry

Classification (MSC91): 34A26, 53C05, 70H35

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