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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 027, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.027 (Mi sigma484) 		 
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
Full-text PDF (330 kB) Citations (3)
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DOI: https://doi.org/10.3842/SIGMA.2010.027
URL: https://emis.mi.ras.ru/journals/SIGMA/2010/027/
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
Bibliographic databases:
Document Type: Article
MSC: 82B23; 37K15; 68R15; 37B15
Language: English
Citation: Taichiro Takagi, “Level Set Structure of an Integrable Cellular Automaton”, SIGMA, 6 (2010), 027, 18 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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