Convergence and Factor Complexity for the Arnoux-Rauzy-Poincaré Algorithm
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چکیده
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.
منابع مشابه
Factor Complexity of S-adic sequences generated by the Arnoux-Rauzy-Poincaré Algorithm
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تاریخ انتشار 2013