arXiv math/05013812005-01-22math.CVmath.DS

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

S. I. Agafonov

备注：: 15 pages, 5 figures

英文摘要：

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.

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