FUNDAMENTALNAYA
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

Abstract

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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, 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.

Location: http://mech.math.msu.su/~fpm/eng/k10/k102/k10203h.htm

Last modified: April 5, 2011