Abstract
We consider a three-web W(1, n, 1) formed by two n-parametric family of curves and one-parameter family of hypersurfaces on a smooth (n + 1)-dimensional manifold. For such webs, the family of adapted frames is defined and the structure equations are found, and geometric objects arising in the third-order differential neighborhood are investigated. It is showed that every system of ordinary differential equations uniquely defines a three-web W(1, n, 1). Thus, there is a possibility to describe some properties of a system of ordinary differential equations in terms of the corresponding three-web W(1, n, 1). In particular, autonomous systems of ordinary differential equations are characterized.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 2, pp. 13–31, 2010.
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Duyunova, A.A. Three-webs defined by a system of ordinary differential equations. J Math Sci 177, 654–667 (2011). https://doi.org/10.1007/s10958-011-0493-5
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DOI: https://doi.org/10.1007/s10958-011-0493-5