Level Set Structure of an Integrable Cellular Automaton
Exactly Solvable and Integrable Systems
2010-04-01 v3 Mathematical Physics
math.MP
Abstract
Based on a group theoretical setting a sort of discrete dynamical system is constructed and applied to a combinatorial dynamical system defined on the set of certain Bethe ansatz related objects known as the rigged configurations. This system is then used to study a one-dimensional periodic cellular automaton related to discrete Toda lattice. It is shown for the first time that the level set of this cellular automaton is decomposed into connected components and every such component is a torus.
Keywords
Cite
@article{arxiv.0906.1410,
title = {Level Set Structure of an Integrable Cellular Automaton},
author = {Taichiro Takagi},
journal= {arXiv preprint arXiv:0906.1410},
year = {2010}
}