Discrete Za and Painleve equations
Sergey I. Agafonov, Alexander I. Bobenko
Abstract
A discrete analogue of the holomorphic map za is studied. It is given by a Schramm's circle pattern with the combinatorics of the square grid. It is shown that the corresponding immersed circle patterns lead to special separatrix solutions of a discrete Painleve equation. Global properties of these solutions, as well as of the discrete za are established.
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