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On the exponential behaviour of non-autonomous difference equations

Part of: Stability theory

Published online by Cambridge University Press:  28 June 2013

Luis Barreira  and
Claudia Valls
Luis Barreira
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal ([email protected]; [email protected])
Claudia Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal ([email protected]; [email protected])
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Abstract

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Given a sequence of matrices (Am)m∈ℕ whose Lyapunov exponents are limits, we show that this asymptotic behaviour is reproduced by the sequences xm+1 = Amxm + fm(xm) for any sufficiently small perturbations fm. We also consider the general case of exponential rates ecρm for an arbitrary increasing sequence ρm. Our approach is based on Lyapunov's theory of regularity.

Keywords

Lyapunov exponentsnon-autonomous difference equationsexponential behavior

MSC classification

Secondary: 34D08: Characteristic and Lyapunov exponents 34D10: Perturbations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 3 , October 2013 , pp. 643 - 656
Copyright
Copyright © Edinburgh Mathematical Society 2013 

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