Asymptotic behavior of discrete holomorphic maps z and log(z)
نویسندگان
چکیده
It is shown that discrete analogs of z 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 z and log(z) at infinity.
منابع مشابه
Hexagonal circle patterns with constant intersection angles and discrete Painlevé and Riccati equations
Hexagonal circle patterns with constant intersection angles mimicking holomorphic maps z and log(z) are studied. It is shown that the corresponding circle patterns are immersed and described by special separatrix solutions of discrete Painlevé and Riccati equations. The general solution of the Riccati equation is expressed in terms of the hypergeometric function. Global properties of these solu...
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