Abstract.Motivated by several patterns arising in molecular biology, in this paper we formulate some interaction systems in micro scale by use of families of maps on the interval. By projecting values of compositions of these maps to a finity subset, we will reconstruct several automata which correspond to macro phenomena. They include Lotka-Volterra cell automaton and the one which produce the lamplighter group. We also study some dynamical properties of such interaction systems of maps.

Received: September 10, 2005

AMS Subject Classification: 92D20, 37B10, 37B15, 37E05, 05C25

Key Words and Phrases: molecular biology, iteration of maps, symbolic dynamics, integrable systems, group actions on trees

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 3