Discrete Z^a and Painleve equations
solv-int
2017-08-25 v1 Complex Variables
Exactly Solvable and Integrable Systems
Abstract
A discrete analogue of the holomorphic map z^a 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 are established.
Keywords
Cite
@article{arxiv.solv-int/9909002,
title = {Discrete Z^a and Painleve equations},
author = {Sergey I. Agafonov and Alexander I. Bobenko},
journal= {arXiv preprint arXiv:solv-int/9909002},
year = {2017}
}
Comments
25 pages, 9 figures