Ukrainian Mathematical Journal

, Volume 48, Issue 10, pp 1600–1608 | Cite as

On the exponential dichotomy of linear difference equations

  • V. I. Tkachenko


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.


Unstable Manifold Stable Manifold Finite Interval Fundamental Matrix Pointwise Convergence 
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© Plenum Publishing Corporation 1997

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  • V. I. Tkachenko

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