EUDML

Let $x = x_{0} x_{1} \dots$ be a fixed point of a substitution on the alphabet $\{a, b\},$ and let $U_{a} = (\begin{matrix} - 1 & - 1 \\ 0 & 1 \end{matrix})$ and $U_{b} = (\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix})$ . We give a complete classification of the substitutions $σ : {\{a, b\}}^{☆}$ according to whether the sequence of matrices ${(U_{x_{0}} U_{x_{1}} \dots U_{x_{n}})}_{n = 0}^{\infty}$ is bounded or unbounded. This corresponds to the boundedness or unboundedness of the oriented walks generated by the substitutions.

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The Spectrum of Dynamical Systems Arising from Substitutions of Constant Length

Marches automatiques

Regularity and irregularity of sequences generated by automata

On the structure of selfgenerating sequences

On the distribution of digits in arithmetic sequences

On the Thue-Morse measure

Mixing Properties of Substitutions

Boundedness of oriented walks generated by substitutions