Substitutions, partial isometries of \(\mathbb{R}\), and actions on trees. (English) Zbl 0936.28013

Holton, Charles; Zamboni, Luca Q.

Bull. Belg. Math. Soc. - Simon Stevin 6, No. 3, 395-411 (1999).

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.

Reviewer: Robert Cowen (Gaborone)

MSC:

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

Keywords:

minimal subshifts; symbolic coding; substitutions