Host, B. Valeurs propres des systèmes dynamiques définis par des substitutions de longuer variable. (Eigenvalues of dynamical systems defined by substitutions of non-constant length). (French) Zbl 0625.28011 Ergodic Theory Dyn. Syst. 6, 529-540 (1986). Dynamical systems defined by substitutions are strictly ergodic systems obtained as the closed orbit (under the shift) of a single sequence u in a shift space over a finite set A. The sequence u is generated by iterating a substitution, i.e., a map \(\zeta\) from A to the set of all non-empty words over A. Such systems can be considered as one of the simplest generalizations of periodic systems. However, their structure is still not completely understood in the case where the words \(\zeta\) (a), \(a\in A\), do not all have the same length. The author makes an important contribution to the solution of this problem by giving a way (at least in principle) to determine the eigenvalues of the \(L^ 2\) operator associated with the dynamical system, generalizing and simplifying previous work in this field. Reviewer: F.M.Dekking Cited in 4 ReviewsCited in 52 Documents MSC: 28D10 One-parameter continuous families of measure-preserving transformations 54H20 Topological dynamics (MSC2010) 28D05 Measure-preserving transformations Keywords:substitutions of non-constant length; eigenvalues of dynamical systems; Dynamical systems defined by substitutions; strictly ergodic systems; shift space; periodic systems PDFBibTeX XMLCite \textit{B. Host}, Ergodic Theory Dyn. Syst. 6, 529--540 (1986; Zbl 0625.28011) Full Text: DOI References: [1] DOI: 10.1007/BF01824809 · Zbl 0256.54026 · doi:10.1007/BF01824809 [2] DOI: 10.1007/BF00534241 · Zbl 0348.54034 · doi:10.1007/BF00534241 [3] DOI: 10.2307/1993856 · Zbl 0121.18002 · doi:10.2307/1993856 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.