Substitution invariant inhomogeneous Beatty sequences
Given a real irrational \(\theta\) and an arbitrary real \(\varphi\), define \(f_n=[(n+1)\theta+\varphi]-[n\theta+\varphi]-[\theta]\). Let \(f_{\theta,\varphi}=\{f_n\}_{n=1}^\infty\) be the sequence with components \(f_n\). The paper aims at giving substitutions \(W\) leaving \(f_{\theta,\varphi}\) invariant, that is \(W(f_{\theta,\varphi})=f_{\theta,\varphi}\), where the substitutions are of the form \(0\mapsto W_0\), \(1\mapsto W_1\) with \(W_0,W_1\) being finite strings of \(0\)'s and \(1\)'s. The paper is a continuation of the article by the author and \textit{A. J. van der Poorten} [Jap. J. Math. 22, 349-354 (1996; Zbl 0868.11015)] where the homogeneous case (\(\varphi=0\)) was considered.
scientific article; zbMATH DE number 1340499