Geometric Representations of Interacting Maps
Tropical geometry is a kind of dynamical scale transform which connects automata with real rational dynamics. Real rational dynamics are deeply studied from global analytic viewpoints. On the other hand, automata appear in various contexts in topology, combinatorics, and integrable systems. In this...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/783738 |
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| _version_ | 1832554796022759424 |
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| author | Tsuyoshi Kato |
| author_facet | Tsuyoshi Kato |
| author_sort | Tsuyoshi Kato |
| collection | DOAJ |
| description | Tropical geometry is a kind of dynamical scale transform which connects automata with real rational dynamics. Real rational dynamics are deeply studied from global analytic viewpoints. On the other hand, automata appear in various contexts in topology, combinatorics, and integrable systems. In this paper we study the analysis of these materials passing through tropical geometry. In particular we discover a new duality on the set of automata which arise from the projective duality in algebraic geometry. |
| format | Article |
| id | doaj-art-b6b4bdc950dc4080b5b1b56301dfe156 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b6b4bdc950dc4080b5b1b56301dfe1562025-02-03T05:50:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/783738783738Geometric Representations of Interacting MapsTsuyoshi Kato0Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, JapanTropical geometry is a kind of dynamical scale transform which connects automata with real rational dynamics. Real rational dynamics are deeply studied from global analytic viewpoints. On the other hand, automata appear in various contexts in topology, combinatorics, and integrable systems. In this paper we study the analysis of these materials passing through tropical geometry. In particular we discover a new duality on the set of automata which arise from the projective duality in algebraic geometry.http://dx.doi.org/10.1155/2010/783738 |
| spellingShingle | Tsuyoshi Kato Geometric Representations of Interacting Maps International Journal of Mathematics and Mathematical Sciences |
| title | Geometric Representations of Interacting Maps |
| title_full | Geometric Representations of Interacting Maps |
| title_fullStr | Geometric Representations of Interacting Maps |
| title_full_unstemmed | Geometric Representations of Interacting Maps |
| title_short | Geometric Representations of Interacting Maps |
| title_sort | geometric representations of interacting maps |
| url | http://dx.doi.org/10.1155/2010/783738 |
| work_keys_str_mv | AT tsuyoshikato geometricrepresentationsofinteractingmaps |