Level Set Structure of an Integrable Cellular Automaton
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2010 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146324 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Level Set Structure of an Integrable Cellular Automaton / T. Takagi // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862580828699099136 |
|---|---|
| author | Takagi, T. |
| author_facet | Takagi, T. |
| citation_txt | Level Set Structure of an Integrable Cellular Automaton / T. Takagi // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-11-26T21:34:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146324 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-26T21:34:50Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Takagi, T. 2019-02-08T20:55:37Z 2019-02-08T20:55:37Z 2010 Level Set Structure of an Integrable Cellular Automaton / T. Takagi // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 82B23; 37K15; 68R15; 37B15 DOI:10.3842/SIGMA.2010.027 https://nasplib.isofts.kiev.ua/handle/123456789/146324 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. This paper is a contribution to the Proceedings of the Workshop “Geometric Aspects of Discrete and UltraDiscrete Integrable Systems” (March 30 – April 3, 2009, University of Glasgow, UK). The full collection is available at http://www.emis.de/journals/SIGMA/GADUDIS2009.html.
 The author thanks Atsuo Kuniba for valuable discuss en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Level Set Structure of an Integrable Cellular Automaton Article published earlier |
| spellingShingle | Level Set Structure of an Integrable Cellular Automaton Takagi, T. |
| title | Level Set Structure of an Integrable Cellular Automaton |
| title_full | Level Set Structure of an Integrable Cellular Automaton |
| title_fullStr | Level Set Structure of an Integrable Cellular Automaton |
| title_full_unstemmed | Level Set Structure of an Integrable Cellular Automaton |
| title_short | Level Set Structure of an Integrable Cellular Automaton |
| title_sort | level set structure of an integrable cellular automaton |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146324 |
| work_keys_str_mv | AT takagit levelsetstructureofanintegrablecellularautomaton |