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

Papaschinopoulos, Garyfalos

Appl. Anal. 40, No. 2-3, 89-109 (1991).

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)

Keywords:

exponential dichotomy; linear difference equation; exponential trichotomy; roughness; bounded solutions

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