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On the exponential behaviour of non-autonomous difference equations

Published online by Cambridge University Press:  28 June 2013

Luis Barreira
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (barreira@math.ist.utl.pt; cvalls@math.ist.utl.pt)
Claudia Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal (barreira@math.ist.utl.pt; cvalls@math.ist.utl.pt)
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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 em for an arbitrary increasing sequence ρm. Our approach is based on Lyapunov's theory of regularity.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2013 

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