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On exponential trichotomy of linear difference equations. (English) Zbl 0687.39003

We start by giving a necessary and sufficient condition in order a linear difference equation to have an exponential trichotomy. The roughness of exponential trichotomy is also proved. A corollary following from the roughness shows that an upper triangular system has an exponential trichotomy if its corresponding diagonal equation has one. Finally we find a relationship between the bounded solutions of a linear equation which has an exponential trichotomy and the bounded solutions of a perturbed equation derived from the linear equation by edding some certain perturbations.
Reviewer: G.Papaschinopoulos

MSC:

39A10 Additive difference equations
39A11 Stability of difference equations (MSC2000)
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