Hexagonal circle patterns with constant intersection angles and discrete Painlevé and Riccati equations

DOI10.1063/1.1586966zbMath1062.37101arXivmath/0301282OpenAlexW3100319749MaRDI QIDQ4833068

Alexander Ivanovich Bobenko, Sergey I. Agafonov

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0301282

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems (37K99) Circle packings and discrete conformal geometry (52C26)

Related Items (5)

Hypergeometric \(\tau\) functions of the \(q\)-Painlevé systems of types \(A_4^{(1)}\) and \((A_1+A_1')^{(1)}\) ⋮ Integrable lattices and their sublattices. II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices ⋮ Geometric description of a discrete power function associated with the sixth Painlevé equation ⋮ Explicit solutions for a nonlinear model on the honeycomb and triangular lattices ⋮ Discrete power functions on a hexagonal lattice I: derivation of defining equations from the symmetry of the Garnier system in two variables

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Circle patterns with the combinatorics of the square grid
• Schwarz's lemma for circle packings
• Discrete Painlevé equations and their appearance in quantum gravity
• The \(C^\infty\)-convergence of hexagonal disk packings to the Riemann map
• Rigidity of infinite disk patterns
• Spiral hexagonal circle packings in the plane
• Hexagonal circle patterns and integrable systems: Patterns with constant angles
• Imbedded circle patterns with the combinatorics of the square grid and discrete Painlevé equations
• The discrete Korteweg-de Vries equation
• Conformally Symmetric Circle Packings: A Generalization of Doyle's Spirals
• Circle packing immersions form regularly exhaustible surfaces
• Circle Packing: Experiments In Discrete Analytic Function Theory

This page was built for publication: Hexagonal circle patterns with constant intersection angles and discrete Painlevé and Riccati equations