On exponential trichotomy of linear difference equations

Abstract

In this paper 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

AMS(MOS):

• 39E10
• 39A11

Keywords:

• Linear difference equations
• exponential dichotomy
• exponential trichotomy
• roughness