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…
Coincidence of invariant measure for the alternate base transformations
Karma Dajani, Niels Langeveld
We characterize all pairs $(β,n),(β^\prime,m)$ such that the alternate and $(β^\prime,m)$-transformations and $K_{(β^\prime,m)}$ have the same absolutely…
On a tree of rational functions related to continued fractions
Niels Langeveld, David Ralston
In this article, we present a binary tree with vertices given by rational functions ; the root and functional derivation of children are inspired by continued fractions.…
On Convergents of Proper Continued Fractions
Niels Langeveld, David Ralston
Proper continued fractions are generalized continued fractions with positive integer numerators and integer denominators with . In this paper we study the streng…