On Closure of a Leaf Invariant Set of a Perturbed System
Author(s):
Nikita Andreevich Begun
St.Petersburg State University
Math.& Mech. Faculty
Postgraduate
matandmeh@gmail.com
Abstract:
In this paper we study small perturbations of differential equations.
For a system of ordinary differential equations the concepts of weakly
hyperbolic set and leaf are introduced. We
show that if the perturbation is small enough, then there is a continuous
mapping that takes a leaf of a unperturbed system into a leaf of the
perturbed one. In addition we show that the union of all the leafs of
the perturbed system is closed.
Bibliography: 4 titles.
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