Asymptotic behavior of discrete holomorphic maps zc, log(z) and discrete Painleve transcedents
S. I. Agafonov
Abstract
It is shown that discrete analogs of zc 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 zc and log(z) at infinity.
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