On critical exponents in fixed points of $k$-uniform binary morphisms
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 1, pp. 41-68.

Let $𝐰$ be an infinite fixed point of a binary $k$-uniform morphism $f$, and let $E\left(𝐰\right)$ be the critical exponent of $𝐰$. We give necessary and sufficient conditions for $E\left(𝐰\right)$ to be bounded, and an explicit formula to compute it when it is. In particular, we show that $E\left(𝐰\right)$ is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets.

DOI: 10.1051/ita:2007042
Classification: 68R15
Keywords: critical exponent, binary $k$-uniform morphism
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Krieger, Dalia. On critical exponents in fixed points of $k$-uniform binary morphisms. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 43 (2009) no. 1, pp. 41-68. doi : 10.1051/ita:2007042. http://www.numdam.org/articles/10.1051/ita:2007042/

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