Hexagonal circle patterns with constant intersection angles and discrete Painlevé and Riccati equations
Year: 2003
Type: article
Abstract: Hexagonal circle patterns with constant intersection angles mimicking holomorphic maps zc 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 solutions, as well as of the discrete zc and log(z), are established.
Source: Journal of Mathematical Physics
DOI: 10.1063/1.1586966
Authors: S. I. Agafonov, A. I. Bobenko
Institution: Technische Universität Berlin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2048162364