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Discrete Dynamical Systems Embedded in Cantor Sets

F. Benatti·A. Verjovski·F. Zertuche
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Abstract

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit $N\to\infty$. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological entropy and Lyapunov exponents through the concept of error-profile. We made explicit calculations both numerical and analytic for well known discrete dynamical models.

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F. Benatti, A. Verjovski, F. Zertuche. 2006-02-15. Discrete Dynamical Systems Embedded in Cantor Sets. https://doi.org/10.1063/1.2171518

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