Hisonal圆模式与可积系统：正则三角格上的多重比模式与Lax方程
Hexagonal circle patterns and integrable systems: Patterns with the multi-ratio property and Lax equations on the regular triangular lattice
摘要：
介绍了晕圈模式，并对其子类进行了详细研究。它的特点是：对于每个圆，它与相邻圆的六个交点的倍数比等于-1。建立了这种模式与正三角格上的可积系统的关系。研究了圆图案的一种B“acklund变换。进一步，引入了上述可积系统的一类等单径解，包括类似于解析函数$z^α$和$\log z$的圆模式.
英文摘要：
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: For every circle the multi-ratio 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 $z^α$ and $\log z$.
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