Abstract
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.
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Tkachenko, V.I. On the exponential dichotomy of linear difference equations. Ukr Math J 48, 1600–1608 (1996). https://doi.org/10.1007/BF02377827
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DOI: https://doi.org/10.1007/BF02377827