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abstract: |
    Any infinite uniformly recurrent word ${\bf u}$ can be written as concatenation of a finite number of return words to a chosen prefix $w$ of ${\bf u}$. Ordering of the return words to $w$ in this concatenation is coded by derivated word $d_{\bf u}(w)$. In 1998, Durand proved that a fixed point ${\bf u}$ of a primitive morphism has only finitely many derivated words $d_{\bf u}(w)$ and each derivated word $d_{\bf u}(w)$ is fixed by a primitive morphism as well. In our article we focus on Sturmian words fixed by a primitive morphism. We provide an algorithm which to a given Sturmian morphism $\psi$ lists the morphisms fixing the derivated words of the Sturmian word ${\bf u} = \psi({\bf u})$. We provide a sharp upper bound on length of the list.

    *Keywords:* Derivated word, Return word, Sturmian morphism, Sturmian word

    *2000MSC:* 68R15
address:
- 'Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Břehová 7, 115 19, Prague 1, Czech Republic'
- 'Department of Applied Mathematics, Faculty of Information Technology, Czech Technical University in Prague, Thákurova 9, 160 00, Prague 6, Czech Republic'
author:
- Karel Klouda
- Kateřina Medková
- 