Rafael Alcaraz Barrera

activity

20192024

collaborators

3 papers

math.DS2024

Topological and dimensional properties of univoque bases in double-base expansions

Yuecai Hu, Rafael Alcaraz Barrera, Yuru Zou

Given two real numbers $q_{0}, q_{1}$ with $q_{0}, q_{1} > 1$ satisfying $q_{0} + q_{1} \geq q_{0} q_{1}$ , we call a sequence $(d_{i})$ with $d_{i} \in {0, 1}$ a $(q_{0}, q_{1})$ -expansion or a double-base expa…

math.DS2021

Chaotic sets and Hausdorff dimension for Lüroth expansions

Rafael Alcaraz Barrera, Gerardo González Robert

We provide new similarities between regular continued fractions and Lüroth series in terms of topological dynamics and Hausdorff dimension. In particular, we establish a complete a…

math.DS2019

On the specification property and synchronisation of unique $q$ -expansions

Rafael Alcaraz Barrera

Given a positive integer $M$ and $q \in (1, M + 1]$ we consider expansions in base $q$ for real numbers $x \in [0, M / q - 1]$ over the alphabet ${0, \dots, M}$ . In par…

Topological and dimensional properties of univoque bases in double-base expansions

Chaotic sets and Hausdorff dimension for Lüroth expansions

On the specification property and synchronisation of unique q-expansions

On the specification property and synchronisation of unique $q$ -expansions