Abstract
We introduce a multidimensional continued fraction algorithm based on Arnoux-Rauzy and Poincaré algorithms, and we study its associated S-adic system. An S-adic system is made of infinite words generated by the composition of infinite sequences of substitutions with values in a given finite set of substitutions, together with some restrictions concerning the allowed sequences of substitutions, expressed in terms of a regular language. We prove that these words have a factor complexity p(n) with lim sup p(n)/n < 3, which provides a proof for the convergence of the associated algorithm by unique ergodicity.
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Berthé, V., Labbé, S. (2013). Convergence and Factor Complexity for the Arnoux-Rauzy-Poincaré Algorithm. In: Karhumäki, J., Lepistö, A., Zamboni, L. (eds) Combinatorics on Words. Lecture Notes in Computer Science, vol 8079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40579-2_10
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DOI: https://doi.org/10.1007/978-3-642-40579-2_10
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