3 papers
math.NT2026
Farey graphs and geodesic expansions of complex continued fractions
Hitoshi Nakada, Rie Natsui, Jörg Thuswaldner
We discuss complex Farey graphs for the Euclidean imaginary quadratic number fields , . We study hyperbolic versions of A. Schmidt's F…
math.DS2025
Nonstationary Markov Partitions and Multidimensional Continued Fraction Algorithms
Pierre Arnoux, Valérie Berthé, Milton Minervino +2
It is well known from results of Sina\uı and Bowen that a hyperbolic toral automorphism admits a Markov partition. Our aim is to generalize this concept to the nonstationary case,…
math.GN2024
Measure and dimension theory of permeable sets and its applications to fractals
Gunther Leobacher, Tapio Rajala, Alexander Steinicke +1
We study {\it permeable} sets. These are sets \(Θ\subset \mathbb{R}^d\) which have the property that each two points \(x,y\in \mathbb{R}^d\) can be connected by a short path \(γ\)…