Running modulus recursions.

Dearden, Bruce; Metzger, Jerry

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Asymptotic behaviour of a difference equation with complex-valued coefficients

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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.

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