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Ordinary differential equations and connections. (English) Zbl 0789.53017
Janyška, Josef (ed.) et al., Differential geometry and its applications. International conference, Brno, Czechoslovakia, 27 Aug. - 2 Sept. 1989. Singapore: World Scientific. 27-32 (1990).
An \((r+1)\)-st order differential equation \(S\) on a manifold \(M\) is a special vector field on the \(r\)-th order tangent bundle \(T^ rM = J^ r_ 0(\mathbb{R},M)\). Generalizing an idea by M. de León and P. R. Rodrigues [Generalized classical mechanics and field theory, North- Holland Math. Stud. 112 (Amsterdam 1985; Zbl 0581.58015)], the author presents several constructions transforming \(S\) into a connection on \(T^ rM \to T^ k M\), \(k < r\).
For the entire collection see [Zbl 0777.00040].
Reviewer: I.Kolář (Brno)

53C05 Connections (general theory)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems