5 citations · 8 across the 9 of their papers we have counts for
14 papers
Coincidence of invariant measure for the alternate base transformations
Karma Dajani, Niels Langeveld
We characterize all pairs such that the alternate and -transformations and have the same absolutely contin…
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…
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…
(non)-matching and (non)-periodicity for -expansions
Cor Kraaikamp, Niels Langeveld
Recently a new class of continued fraction algorithms, the )-expansions, was introduced for each , and . Each of these continue…
A Renormalization Scheme for Semi-Regular Continued Fractions
Niels Langeveld, David Ralston
In this article we study a renormalization scheme with which we find all semi-regular continued fractions of a number in a natural way. We define two maps, T_slow and T_fast: these…
Intermediate -shifts as greedy -shifts with a hole
Niels Langeveld, Tony Samuel
We show that every intermediate -transformation is topologically conjugate to a greedy -transformation with a hole at zero, and provide a counterexample illustrating that the…
Generalizations of Sturmian sequences associated with -continued fraction algorithms
Niels Langeveld, Lucía Rossi, Jörg M. Thuswaldner
Given a positive integer and irrational between zero and one, an -continued fraction expansion of is defined analogously to the classical continued fraction expansio…
Alternating -expansions
Karma Dajani, Niels Langeveld
We introduce a family of maps generating continued fractions where the digit in the numerator is replaced cyclically by some given non-negative integers . We…
Natural extensions and entropy of -continued fraction expansions with odd partial quotients
Yusuf Hartono, Cor Kraaikamp, Niels Langeveld +1
In an article (which we will refer to as [BM]) of Boca and the fourth author of this paper, a new class of continued fraction expansions with odd partial quotients, parameterized b…
Tanaka-Ito -continued fractions and matching
Carlo Carminati, Niels Langeveld, Wolfgang Steiner
Two closely related families of -continued fractions were introduced in 1981: by Nakada on the one hand, by Tanaka and Ito on the other hand. The behavior of the entropy as a fu…
Matching for a family of infinite measure continued fraction transformations
Charlene Kalle, Niels Langeveld, Marta Maggioni +1
As a natural counterpart to Nakada's -continued fraction maps, we study a one-parameter family of continued fraction transformations with an indifferent fixed point. We prove th…
The -transformation with a hole at 0
Charlene Kalle, Derong Kong, Niels Langeveld +1
For the -transformation is defined by . For let be the survivor set of with hole giv…
Invariant measures for continued fraction algorithms with finitely many digits
Cor Kraaikamp, Niels Langeveld
In this paper we consider continued fraction (CF) expansions on intervals different from . For every in such interval we find a CF expansion with a finite number of poss…