On the exponential dichotomy of linear difference equations - Tkachenko, V. I. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We consider a system of linear difference equationsx n+1 =A (n)xn in anm-dimensional real or complex spaceVsum with detA(n) = 0 for some or alln εZ. We study the exponential dichotomy of this system and prove that if the sequence A(n) is Poisson stable or recurrent, then the exponential dichotomy on the semiaxis implies the exponential dichotomy on the entire axis. If the sequence A (n) is almost periodic and the system has exponential dichotomy on the finite interval k, ...,k +T,k εZ, with sufficiently largeT, then the system is exponentially dichotomous onZ.