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non-autonomous difference equations

Proceedings of the Edinburgh Mathematical Society (1)

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On the exponential behaviour of non-autonomous difference equations
Part of
- Stability theory
Luis Barreira, Claudia Valls
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013

Published online by Cambridge University Press:

28 June 2013, pp. 643-656
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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.