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Substitutions, partial isometries of \(\mathbb{R}\), and actions on trees. (English) Zbl 0936.28013
The authors show that the minimal subshifts generated by a primitive substitution provides a symbolic coding of the dynamics of the partial isometries associated to each real geometric realization of the substitutions. They use this result to give a detailed investigation of the dynamical and structural properties of the system.

MSC:
28D05 Measure-preserving transformations
28A78 Hausdorff and packing measures
37A20 Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations
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