Hexagonal circle patterns and integrable systems: Patterns with the multiratio property and Lax equations on the regular triangular lattice
Abstract
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multiratio of its six intersection points with neighboring circles is equal to 1. The relation of such patterns with an integrable system on the regular triangular lattice is established. A kind of a B"acklund transformation for circle patterns is studied. Further, a class of isomonodromic solutions of the aforementioned integrable system is introduced, including circle patterns analogons to the analytic functions $z^\alpha$ and $\log z$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2001
 DOI:
 10.48550/arXiv.math/0104244
 arXiv:
 arXiv:math/0104244
 Bibcode:
 2001math......4244B
 Keywords:

 Mathematics  Complex Variables;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 43 pages, 13 figures