Level Set Structure of an Integrable Cellular Automaton

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.

References in corpus (6)

• Fundamental Cycle of a Periodic Box-Ball System
• On a Periodic Soliton Cellular Automaton
• Bethe ansatz and inverse scattering transform in a periodic box-ball system
• The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function
• Ultradiscretization of the solution of periodic Toda equation
• Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for A^{(1)}_n

Cited by in corpus (3)

• Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
• Bethe Ansatz, Inverse Scattering Transform and Tropical Riemann Theta Function in a Periodic Soliton Cellular Automaton for A^{(1)}_n
• Combinatorial aspects of the conserved quantities of the tropical periodic Toda lattice