Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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.

References:

1. Begun N. A. Ob ustoichivosti listovih invariantnih mnogestv dvumernih periodicheskih system // Vestnik Sankt-Peterburgskogo universiteta, Ser. 1. 2012. vip. 4. p. 3-12
2. V. A. Pliss and G. R. Sell. Perturbations of attractors of differential equations // J. Differential Equations. 1991. Vol. 92. P. 100-124
3. V. A. Pliss and G. R. Sell. Approximation Dynamics and the Stability of Invariant Sets // J. Differential Equations. 1997. Vol. 149. P. 1-51
4. Pliss V. A. Integral sets of periodical systems of differential equations (in Russian) M. : Nauka. 1976. 304 с

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