D. Ralston

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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.DS2025

Birkhoff Measures, Birkhoff Sums, and Discrepancies

D. Ralston, F. M. Tangerman, J. J. P. Veerman +1

We study the distribution of a sequence of points in the circle generated by rotations by a fixed irrational number $ρ$ with initial condition $x_{0}$ , that is: ${x_{0} + i ρ}_{i = 1}^{n}$ .…

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…