Discrete $Z^γ$: embedded circle patterns with the combinatorics of the square grid and discrete Painlevé equations

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dc.creatorAgafonov, S. I.
dc.date2001-10-17
dc.date2003-02-11
dc.date.accessioned2026-07-07T05:33:43Z
dc.date.available2026-07-07T05:33:43Z
dc.descriptionA discrete analog 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 embedded 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.
dc.description12 pagees 4 figures
dc.identifierhttps://arxiv.org/abs/nlin/0110030
dc.identifierhttp://arxiv.org/abs/nlin/0110030
dc.identifierTheor. and Math. Physics, V 134, N 1, 2003, pp. 3--13
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/80099
dc.subjectExactly Solvable and Integrable Systems
dc.titleDiscrete $Z^γ$: embedded circle patterns with the combinatorics of the square grid and discrete Painlevé equations
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