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A reduction principle for topological classification of nonautonomous differential equations

Published online by Cambridge University Press:  14 November 2011

Nguyen Van Minh
Nguyen Van Minh
Affiliation:
Chair of Mathematical Methods in Control Theory, Department of Mathematics and Mechanics, Belorussian State University, Minsk 220 080, Belorussia
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Synopsis

The paper is concerned with equations of the form x' = A(t)x +f(t, x), where A is a continuous matrix function defined on ℝ, f is a continuous vector-valued function of (t, x) with f(t, 0) = 0. It is proved that if x' = A(t)x has an exponential trichotomy, A is bounded and f satisfies the Lipschitz condition with coefficient sufficiently small, then these equations are topologically equivalent to the systems of equations of the form , where B, g satisfy the same conditions as A, f.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 4 , 1993 , pp. 621 - 632
Copyright
Copyright © Royal Society of Edinburgh 1993

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