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For difference equations in Banach spaces, we consider a generalization of the notion of exponential dichotomy, usually called trichotomy in the literature, for which the behaviors in $$\mathbb {Z}^+$$ Z + and $$\mathbb {Z}^-$$ Z - are still exponential but need not agree at the origin. Our main aim is to show that this exponential behavior is robust, in the sense that it...
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