Discrete Dynamical Systems Embedded in Cantor Sets
Fabio Benatti, Istituto Nazionale, Fisica Nucleare, Sezione Di Trieste, Alberto Verjovsky, Federico Zertuche · 2006
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 → ∞. 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.