Hexagonal circle patterns with constant intersection angles and discrete Painleve and Riccati equations

Details Hexagonal circle patterns with constant intersection angles and discrete Painleve and Riccati equations Hexagonal circle patterns with constant intersection angles and discrete Painleve and Riccati equations

2003-01-24

arxiv.org/abs/math/0301282v2

Mathematics

Complex Variables

18 pages, 6 figures

Scientific paper

10.1063/1.1586966

Hexagonal circle patterns with constant intersection angles mimicking holomorphic maps z^c and log(z) are studied. It is shown that the corresponding circle patterns are immersed and described by special separatrix solutions of discrete Painleve and Riccati equations. The general solution of the Riccati equation is expressed in terms of the hypergeometric function. Global properties of these solutions, as well as of the discrete z^c and log(z), are established.

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