Cellular Automata vs. Quasisturmian Shifts
Abstract
If L=ZD and A is a finite set, then AL is a compact space. A cellular automaton (CA) is a continuous transformation F:AL--> AL that commutes with all shift maps. A quasisturmian (QS) subshift is a shift-invariant subset obtained by mapping the trajectories of an irrational torus rotation through a partition of the torus. The image of a QS shift under a CA is again QS. We study the topological dynamical properties of CA restricted to QS shifts, and compare them to the properties of CA on the full shift AL. We investigate injectivity, surjectivity, transitivity, expansiveness, rigidity, fixed/periodic points, and invariant measures. We also study `chopping': how iterating the CA fragments the partition generating the QS shift.
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