zbMATH — the first resource for mathematics

On the rank of a class of bijective substitutions. (English) Zbl 0711.28007
It was conjectured by M. K. Mentzen that for any pair of rational numbers (k,n), where \(k\leq n\), it is possible to construct an ergodic automorphism with rank n and spectral multiplicity k. The case (1,n) was solved by M. K. Mentzen [Bull. Pol. Acad. Sci., Math. 35, 417-424 (1987; Zbl 0675.28006)]. In this paper it is shown that a general class of bijective substitutions over r symbols has rank r and this theorem is used to solve Mentzens problem for the case (2,n).
Reviewer: R.Cowen

28D05 Measure-preserving transformations
Full Text: DOI EuDML