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Approximation of attractors for nongradient systems

Published online by Cambridge University Press:  14 November 2011

I. N. Kostin
I. N. Kostin
Affiliation:
Steklov Mathematical Institute, St. Petersburg Branch, 27 Fontanka, St. Petersburg 191011, Russia e-mail: kostin@pdmi.ras.ru
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Abstract

The problem of approximation of attractors for semidynamical systems (SDSs) in a metric space is studied. Let some (exact) SDS possessing an attractor M be inaccurately defined, i.e. let another (approximate) SDS, which is close in some sense to the exact one, be given. The problem is to construct a set , which is close to M in the Hausdorff metric.

The suggested procedure for constructing is finite, which makes it possible to use it in computations. The results obtained are suitable for numerical approximation of attractors for a rather large class of semidynamical systems, including ones generated by the Lorenz equations and the Navier–Stokes equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 4 , 1995 , pp. 739 - 758
Copyright
Copyright © Royal Society of Edinburgh 1995

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