Imbedded Circle Patterns with the Combinatorics of the Square Grid and Discrete Painlevé Equations

نویسنده

Sergey I. Agafonov

چکیده

A discrete analogue of the holomorphic map z γ is studied. It is given by Schramm's circle pattern with the combinatorics of the square grid. It is shown that the corresponding circle patterns are imbedded and described by special separatrix solutions of discrete Painlevé equations. Global properties of these solutions, as well as of the discrete z γ , are established.

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