Asymptotic behavior of discrete holomorphic maps zc and log(z)

DOI

10.2991/jnmp.2005.12.s2.1How to use a DOI?

Abstract

It is shown that discrete analogs of zc and log(z), defined via particular "integrable" circle patterns, have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painlevé-II equations, asymptotics of these solutions providing the behaviour of discrete zc and log(z) at infinity.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Sergey I. Agafonov
PY  - 2005
DA  - 2005/12/01
TI  - Asymptotic behavior of discrete holomorphic maps zc and log(z)
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 14
VL  - 12
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s2.1
DO  - 10.2991/jnmp.2005.12.s2.1
ID  - Agafonov2005
ER  -