Gerardo González Robert

collaborators

4 papers

math.DS2023

Restricted slowly growing digits for infinite iterated function systems

Gerardo González Robert, Mumtaz Hussain, Nikita Shulga +1

For an infinite iterated function system $f$ on $[0, 1]$ with an attractor $Λ (f)$ and for an infinite subset $D \subseteq N$ , consider the set \[ \mathbb E…

math.NT2023

Complex numbers with a prescribed order of approximation and Zaremba's conjecture

Gerardo González Robert, Mumtaz Hussain, Nikita Shulga

Given $b = - A \pm i$ with $A$ being a positive integer, we can represent any complex number as a power series in $b$ with coefficients in $A = {0, 1, \dots, A^{2}}$ . We prove th…

math.NT2023

Metrical properties of weighted products of consecutive Lüroth digits

Adam Brown-Sarre, Gerardo González Robert, Mumtaz Hussain

The Lüroth expansion of a real number $x \in (0, 1]$ is the series \[ x= \frac{1}{d_1} + \frac{1}{d_1(d_1-1)d_2} + \frac{1}{d_1(d_1-1)d_2(d_2-1)d_3} + \cdots, \] with $d_j\in\mathbb{…

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…