4 papers
Convergence and combinatorics of the Reverse algorithm
Hiroaki Ito, Niels Langeveld, Jörg Thuswaldner
We study the Reverse algorithm, a multidimensional continued fraction algorithm, which is not unimodular. We show that the Reverse algorithm is ergodic and, by proving that its sec…
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…
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,…
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 \(Î\subset \mathbb{R}^d\) which have the property that each two points \(x,y\in \mathbb{R}^d\) can be connected by a short path \(γ\…