English

Hexagonal Circle Patterns and Integrable Systems. Patterns with Constant Angles

Complex Variables 2007-05-23 v1 Exactly Solvable and Integrable Systems

Abstract

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 zcz^c and logz\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.

Keywords

Cite

@article{arxiv.math/0109018,
  title  = {Hexagonal Circle Patterns and Integrable Systems. Patterns with Constant Angles},
  author = {Alexander I. Bobenko and Tim Hoffmann},
  journal= {arXiv preprint arXiv:math/0109018},
  year   = {2007}
}

Comments

33 pages, 14 figures