N. Langeveld

activity

20162026

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7 papers · 1 filter

math.DS2026

Coincidence of invariant measure for the alternate base transformations

Karma Dajani, Niels Langeveld

We characterize all pairs $(β, n), (β^{'}, m)$ such that the alternate $(β, n)$ and $(β^{'}, m)$ -transformations $K_{(β, n)}$ and $K_{(β^{'}, m)}$ have the same absolutely contin…

math.DS2025

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 $p (x) / q (x)$ ; the root and functional derivation of children are inspired by continued fractions.…

math.DS2024

On Convergents of Proper Continued Fractions

Niels Langeveld, David Ralston

Proper continued fractions are generalized continued fractions with positive integer numerators $a_{i}$ and integer denominators with $b_{i} \geq a_{i}$ . In this paper we study the streng…

math.DS2021

Natural extensions and entropy of $α$ -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…

math.DS2019

Matching for a family of infinite measure continued fraction transformations

Charlene Kalle, Niels Langeveld, Marta Maggioni +1

As a natural counterpart to Nakada's $α$ -continued fraction maps, we study a one-parameter family of continued fraction transformations with an indifferent fixed point. We prove th…

math.DS2018

The $β$ -transformation with a hole at 0

Charlene Kalle, Derong Kong, Niels Langeveld +1

For $β \in (1, 2]$ the $β$ -transformation $T_{β} : [0, 1) \to [0, 1)$ is defined by $T_{β} (x) = β x (mod 1)$ . For $t \in [0, 1)$ let $K_{β} (t)$ be the survivor set of $T_{β}$ with hole $(0, t)$ giv…