Substitution invariant sturmian bisequences

Complete Characterization of Substitution Invariant Sturmian Sequences

We provide a complete characterization of substitution invariant inhomogeneous bidirectional pointed Sturmian sequences. The result is analogous to that obtained by Berthé et al. [5] and Yasutomi [21] for one-directional Sturmian words. The proof is constructive, based on the geometric representation of Sturmian words by a cut-and-project scheme.

On substitution invariant Sturmian words: an application of Rauzy fractals

Sturmian words are infinite words that have exactly n+ 1 factors of length n for every positive integer n. A Sturmian word sα,ρ is also defined as a coding over a two-letter alphabet of the orbit of point ρ under the action of the irrational rotation Rα : x 7→ x+ α (mod 1). A substitution fixes a Sturmian word if and only if it is invertible. The main object of the present paper is to investiga...

Heaviness in Symbolic Dynamics: Substitution and Sturmian Systems

Heaviness refers to a sequence of partial sums maintaining a certain lower bound and was recently introduced and studied in [11]. After a review of basic properties to familiarize the reader with the ideas of heaviness, general principles of heaviness in symbolic dynamics are introduced. The classical Morse sequence is used to study a specific example of heaviness in a system with nontrivial ra...

Substitution Invariant Beatty Sequences

with θ irrational and taken to satisfy 0 < θ < 1; plainly this may be assumed without loss of generality. Evidently (fn) is a sequence of zeros and ones. Denote by w0 and w1 words on the alphabet {0, 1} ; that is, finite strings in the letters 0 and 1. Then the sequence (fn) is said to be invariant under the substitution W given by W : 0 −→ w0, 1 −→ w1, if the infinite strings fθ = f1f2f3 . . ....

Substitution invariant cutting sequences