2019
Том 71
№ 11

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On the exponential dichotomy of linear difference equations

Tkachenko V. I.

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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.

English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 10, pp 1600-1608.

Citation Example: Tkachenko V. I. On the exponential dichotomy of linear difference equations // Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1409-1416.

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