Level Set Structure of an Integrable Cellular Automaton

Details Level Set Structure of an Integrable Cellular Automaton Level Set Structure of an Integrable Cellular Automaton

2009-06-08

arxiv.org/abs/0906.1410v3

SIGMA 6 (2010), 027, 18 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.3842/SIGMA.2010.027

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.

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