Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 027, 18 pages      arXiv:0906.1410      http://dx.doi.org/10.3842/SIGMA.2010.027
Contribution to the Proceedings of the Workshop “Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems”

Level Set Structure of an Integrable Cellular Automaton

Taichiro Takagi
Department of Applied Physics, National Defense Academy, Kanagawa 239-8686, Japan

Received October 23, 2009, in final form March 15, 2010; Published online March 31, 2010

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.

Key words: periodic box-ball system; rigged configuration; invariant torus.

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