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Discrete dynamical systems embedded in Cantor sets

2006; American Institute of Physics; Volume: 47; Issue: 2 Linguagem: Inglês

10.1063/1.2171518

1527-2427

Fabio Benatti, Alberto Verjovsky, Federico Zertuche,

Chaos control and synchronization

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.