$N$-continued fractions and $S$-adic sequences

Abstract: Given the $N$-continued fraction of a number $x$, we construct $N$-continued fraction sequences in the same spirit as Sturmian sequences can be constructed from regular continued fractions. These sequences are infinite words over a two letter alphabet obtained as the limit of a directive sequence of certain substitutions (they are S-adic sequences). By viewing them as a generalisation of Sturmian sequences it is natural to study balancedness. We will see that the sequences we construct are not 1-balanced but C-balanced for $C=N^2$. Furthermore, we construct a dual sequence which is related to the natural extension of the $N$-continued fraction algorithm. This talk is joint work with Lucía Rossi and Jörg Thuswaldner.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

Series comments: Description: Online seminar on numeration systems and related topics

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