Discretization of phase space usually nullifies chaos in dynamical systems. We show that if randomness is associated with discretization dynamical chaos may survive and be indistinguishable from that of the original chaotic system, when an entropic, coarse-grained analysis is performed. Relevance of this phenomenon to the problem of quantum chaos is discussed.
Falcioni, M., Vulpiani, A., Mantica, G., Pigolotti, S. Coarse-grained probabilistic automata mimicking chaotic systems. "Physical review letters", 24 Juliol 2003, vol. 91, núm. 4, p. 044101-1-04410-4.