M. D. Vries

activity

20062010

most citedUnique expansions of real numbers

3 citations · 3 across the 5 of their papers we have counts for

collaborators

5 papers

math.NT2010

Optimal expansions in non-integer bases

Karma Dajani, Martijn de Vries, Vilmos Komornik +1

For a given positive integer $m$ , let $A = {0, 1, ..., m}$ and $q \in (m, m + 1)$ . A sequence $(c_{i}) = c_{1} c_{2} ...$ consisting of elements in $A$ is called an expansion of $x$ if $\sum_{i…

math.NT2008

On the number of unique expansions in non-integer bases

Martijn de Vries

Let $q > 1$ be a real number and let $m = m (q)$ be the largest integer smaller than $q$ . It is well known that each number $x \in J_{q} := [0, \sum_{i = 1}^{\infty} m q^{- i}]$ can be writt…

math.DS2006

Invariant densities for random $β$ -expansions

K. Dajani, M. de Vries

Let $β > 1$ be a non-integer. We consider expansions of the form $\sum_{i = 1}^{\infty} d_{i} β^{- i}$ , where the digits $(d_{i})_{i \geq 1}$ are generated by means of a Borel map $K_{β}$ def…

math.NT2006

A property of algebraic univoque numbers

M. de Vries

Consider the set $\uu$ of real numbers $q \geq 1$ for which only one sequence $(c_{i})$ of integers $0 \leq c_{i} \leq q$ satisfies the equality $\sum_{i = 1}^{\infty} c_{i} q^{- i} = 1$ . In t…

math.NT2006★ 3 cited

Unique expansions of real numbers

Martijn de Vries, Vilmos Komornik

It was discovered some years ago that there exist non-integer real numbers $q > 1$ for which only one sequence $(c_{i})$ of integers $c_{i} \in [0, q)$ satisfies the equality $\sum_{i=1}^…

Optimal expansions in non-integer bases

On the number of unique expansions in non-integer bases

Invariant densities for random β-expansions

A property of algebraic univoque numbers

Unique expansions of real numbers

Invariant densities for random $β$ -expansions