Geodesic
Asymptotic behaviour of a difference equation with complex-valued coefficients
Archivum mathematicum, Tome 41 (2005) no. 3, pp. 311-323.

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The asymptotic behaviour for solutions of a difference equation $z_n = f(n,z_n)$, where the complex-valued function $f(n,z)$ is in some meaning close to a holomorphic function $h$, and of a Riccati difference equation is studied using a Lyapunov function method. The paper is motivated by papers on the asymptotic behaviour of the solutions of differential equations with complex-valued right-hand sides.
Classification : 39A11
Keywords: difference equations; asymptotic behaviour; Lyapunov functions 
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Kalas, Josef. Asymptotic behaviour of a difference equation with complex-valued coefficients. Archivum mathematicum, Tome 41 (2005) no. 3, pp. 311-323. http://geodesic.mathdoc.fr/item/ARM_2005__41_3_a6/