A first integrability result for Miquel dynamics
Dynamical Systems
2018-05-22 v2 Algebraic Geometry
Exactly Solvable and Integrable Systems
Abstract
Miquel dynamics is a discrete-time dynamical system on the space of square-grid circle patterns. For biperiodic circle patterns with both periods equal to two, we show that the dynamics corresponds to translation on an elliptic curve, thus providing the first integrability result for this dynamics. The main tool is a geometric interpretation of the addition law on the normalization of binodal quartic curves.
Keywords
Cite
@article{arxiv.1801.01082,
title = {A first integrability result for Miquel dynamics},
author = {Alexey Glutsyuk and Sanjay Ramassamy},
journal= {arXiv preprint arXiv:1801.01082},
year = {2018}
}
Comments
14 pages, 2 figures