I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2010, VOLUME 16, NUMBER 2, PAGES 13-31
Three-webs defined by a system of ordinary differential equations
A. A. Duyunova
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We consider a three-web formed by two
family of curves and one-parameter family of hypersurfaces on
a smooth -dimensional manifold.
For such webs, the family of adapted frames is defined and the
structure equations are found, 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 .
Thus, there is a possibility to describe some properties of
a system of ordinary differential equations in terms of the
corresponding three-web .
In particular, autonomous systems of ordinary differential equations
Last modified: April 5, 2011