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Quasigroups on manifolds with trajectories. (English) Zbl 0844.22010
Shelekhov, A. (ed.), Webs and quasigroups. Dedicated to the 60th birthday of Prof. Dr. Vladislav V. Goldberg. Tver: Tver State University. 88-96 (1995).
The notion of a manifold with trajectories is introduced as a one-parameter family of local quasigroups, reflecting properties of solutions of a second order differential equation on a manifold. Some special properties of the differential equation are characterized by the algebraical identities in the manifold with trajectories. Affine connections are associated with a manifold with trajectories. Mechanic systems are considered from this viewpoint.
For the entire collection see [Zbl 0841.00012].
MSC:
22A99 Topological and differentiable algebraic systems
34A26 Geometric methods in ordinary differential equations
53B99 Local differential geometry
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