Rie Natsui

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20072026

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math.DS2024

A new class of $α$ -Farey maps and an application to normal numbers

Karma Dajani, Cornelis Kraaikamp, Hitoshi Nakada +1

We define two types of the $α$ -Farey maps $F_{α}$ and $F_{α, ♭}$ for $0 < α < \frac{1}{2}$ , which were previously defined only for $\frac{1}{2} \leq α \leq 1$ by R.~Natsui (2004).…

math.DS2014

Farey map, Diophantine approximation and Bruhat-Tits tree

Dong Han Kim, Seonhee Lim, Hitoshi Nakada +1

Based on Broise-Alamichel and Paulin's work on the Gauss map corresponding to the principal convergents, we continue the study of the Gauss map via Farey maps to contain all the in…

math.DS2007

Generalized Brjuno functions associated to $α$ -continued fractions

Laura Luzzi, Stefano Marmi, Hitoshi Nakada +1

For αin the interval [0,1], we consider the one-parameter family of α-continued fraction maps, which include the Gauss map (α=1) and the nearest integer (α=1/2) and by-excess (α=0)…

A new class of α-Farey maps and an application to normal numbers

Farey map, Diophantine approximation and Bruhat-Tits tree

Generalized Brjuno functions associated to α-continued fractions

A new class of $α$ -Farey maps and an application to normal numbers

Generalized Brjuno functions associated to $α$ -continued fractions