This article is cited in 3 papers

Level Set Structure of an Integrable Cellular Automaton

Taichiro Takagi

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

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

MSC: 82B23; 37K15; 68R15; 37B15

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

Language: English

DOI: 10.3842/SIGMA.2010.027

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ArXiv: 0906.1410