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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)

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