Classification of Finite Dynamical Systems

Details Classification of Finite Dynamical Systems Classification of Finite Dynamical Systems

2001-12-20

arxiv.org/abs/math/0112216v1

Mathematics

Dynamical Systems

12 pages, 3 figures

Scientific paper

This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by composing functions defined on the coordinates. The classification is in terms of the dependency relations among the coordinate functions. It suggests a natural notion of the linearization of a system. Furthermore, it contains a sharp upper bound on the number of systems in terms of the dependencies among the coordinate functions. This upper bound generalizes an upper bound for sequential dynamical systems.

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