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

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Agafonov, S. I. (2005)
  • Subject: Mathematics - Dynamical Systems | Mathematics - Complex Variables | 52C26 Circle packings and discrete conformal geometry

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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