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This article is cited in 3 scientific papers (total 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.
Received: October 23, 2009; in final form March 15, 2010; Published online March 31, 2010
Citation:
Taichiro Takagi, “Level Set Structure of an Integrable Cellular Automaton”, SIGMA, 6 (2010), 027, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma484 https://www.mathnet.ru/eng/sigma/v6/p27
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Abstract page: | 178 | Full-text PDF : | 39 | References: | 32 |
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