International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 783738, 48 pages
Research Article

Geometric Representations of Interacting Maps

Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan

Received 17 February 2010; Revised 6 June 2010; Accepted 13 June 2010

Academic Editor: Misha Rudnev

Copyright © 2010 Tsuyoshi Kato . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.