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SIGMA, 2010, Volume 6, 027, 18 pages (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

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

DOI: https://doi.org/10.3842/SIGMA.2010.027

Full text: PDF file (330 kB)
Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/027/
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Bibliographic databases:

ArXiv: 0906.1410
MSC: 82B23; 37K15; 68R15; 37B15
Received: October 23, 2009; in final form March 15, 2010; Published online March 31, 2010
Language:

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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\by Taichiro Takagi
\paper Level Set Structure of an Integrable Cellular Automaton
\jour SIGMA
\yr 2010
\vol 6
\papernumber 027
\totalpages 18
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84896062833}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Inoue R., Kuniba A., Takagi T., “Integrable structure of box-ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry”, Journal of Physics A-Mathematical and Theoretical, 45:7 (2012), 073001  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Takagi T., “Commuting Time Evolutions in the Tropical Periodic Toda Lattice”, J. Phys. Soc. Jpn., 81:10 (2012), 104005  crossref  adsnasa  isi  scopus
    3. Takagi T., “Combinatorial Aspects of the Conserved Quantities of the Tropical Periodic Toda Lattice”, J. Phys. A-Math. Theor., 47:39 (2014), 395201  crossref  mathscinet  zmath  adsnasa  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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