Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents

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It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.
15 pages, 5 figures

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Complex Variables, Dynamical Systems, 52C26 Circle packings and discrete conformal geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/73933

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501381
 http://arxiv.org/abs/math/0501381

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arXiv