DISCRETE RICCATI EQUATION, HYPERGEOMETRIC FUNCTIONS AND CIRCLE PATTERNS OF SCHRAMM TYPE

被引：5
|
作者：
Agafonov, S. I. [1 ]
机构：
[1] Univ Halle Wittenberg, Inst Algebra & Geometrie, D-06099 Halle, Germany
来源：
GLASGOW MATHEMATICAL JOURNAL | 2005年 / 47A卷
基金：
英国工程与自然科学研究理事会;
关键词：
D O I：
10.1017/S0017089505002247
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Square grid circle patterns with prescribed intersection angles, mimicking holomorphic maps z(gamma) and log(z) are studied. It is shown that the corresponding circle patterns are embedded and described by special separatrix solutions of discrete Painlev'e and Riccati equations. The general solution of this Riccati equation is expressed in terms of the hypergeometric function. Global properties of these solutions, as well as of the discrete z(gamma) and log(z), are established.
引用
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页码：1 / 16
页数：16
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