Hexagonal Circle Patterns and Integrable Systems. Patterns with Constant Angles

Details Hexagonal Circle Patterns and Integrable Systems. Patterns with Constant Angles Hexagonal Circle Patterns and Integrable Systems. Patterns with Constant Angles

2001-09-04

arxiv.org/abs/math/0109018v1

Mathematics

Complex Variables

33 pages, 14 figures

Scientific paper

Hexagonal circle patterns with constant intersection angles are introduced and studied. It is shown that they are described by discrete integrable systems of Toda type. Conformally symmetric patterns are classified. Circle pattern analogs of holomorphic mappings $z^c$ and $\log z$ are constructed as special isomonodromic solutions. Circle patterns studied in the paper include Schramm's circle patterns with the combinatorics of the square grid as a special case.

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