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

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

2005-01-22

arxiv.org/abs/math/0501381v1

Mathematics

Complex Variables

15 pages, 5 figures

Scientific paper

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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