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In this paper, the dynamical behaviors of elementary cellular automata (ECA) rule 88 are studied from the viewpoint of symbolic dynamics. Based on the results derived from the finite case, it is shown that there exist three different Bernoulli-measure subsystems of rule 88 in the space of bi-infinite symbolic sequences. The relationships of these three subsystems and the existence of fixed points...
In this paper, a class of linear maps on the 2-torus are discussed. Discussions are focused on the case that the maps are parabolic. It is shown that the maximal invariant set for a 2-torus parabolic map is indeed invariant, and is almost closed, and the Lebesgue measure restricted to a maximal invariant set is invariant. Under this invariant measure, all Lyapunov exponents of a parabolic map are...
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