Hexagonal circle patterns and integrable systems: Patterns with the multi-ratio property and Lax equations on the regular triangular lattice

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dc.creatorBobenko, A. I.
dc.creatorHoffmann, T.
dc.creatorSuris, Yu. B.
dc.date2001-04-25
dc.date.accessioned2026-07-07T04:41:27Z
dc.date.available2026-07-07T04:41:27Z
dc.descriptionHexagonal 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 $\log z$.
dc.description43 pages, 13 figures
dc.identifierhttps://arxiv.org/abs/math/0104244
dc.identifierhttp://arxiv.org/abs/math/0104244
dc.identifierIntern. Math. Research Notices, 2002, No 3, p.111-164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61364
dc.subjectComplex Variables
dc.subjectExactly Solvable and Integrable Systems
dc.titleHexagonal circle patterns and integrable systems: Patterns with the multi-ratio property and Lax equations on the regular triangular lattice
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