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A perturbation theorem for exponential dichotomies

Published online by Cambridge University Press:  14 November 2011

Kenneth J. Palmer
Kenneth J. Palmer
Affiliation:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124, U.S.A.
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Synopsis

Suppose the linear equation x' = A(t)x has an exponential dichotomy and suppose B(t) is close to A(t) in the following sense: on any interval of length 2T, B(t) is close to some translate A(t + τ) of A(t) (actually the conditions in the paper are slightly weaker than this). Then if T is sufficiently large, the equation y' = B(t)y also has an exponential dichotomy. This generalises the usual roughness theorem for exponential dichotomies.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 1-2 , 1987 , pp. 25 - 37
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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