Ir.Dr. Niels Langeveld

Research interests (keywords)

  • Ergodic theory and dynamical systems
  • Numeration systems (in particular, beta-expansions and continued fractions)
  • Open dynamical systems
  • Symbolic dynamics
  • Interval maps
  • Natural extensions
  • Matching

 

natextNfininte
An example of a domain of a natural extension related to N-expansions with finitely many digits (from [2]).
intervalsbetacropcropwithcolours
Some basic intervals for which periodic points (corresponding to the label) are isolated in the bifurcation set. The largest intervals correspond to Farey words (see [3] for more information).
from0to1biglargerintervals
A visualization of the matching intervals of Tanaka Ito alpha-continued fractions. The fraction displayed gives the pseudo center of the matching interval, the color gives whether the matching index is smaller, equal or larger than 0. The height is determined by the length of the interval (picture relates to [5]).

Publications

[11] A renormalization scheme for semi-regular continued fractions 
Monatsh Math (2024), with David Ralston.

[10] On matching and periodicity for (N,α)-expansions
Ramanujan J. (2024), with Cor Kraaikamp.

[9] Natural extensions and entropy of α-continued fraction expansions with odd partial quotients 
Discrete Contin. Dyn. Syst. 43 (2023), no. 8, 2852–2888., with Yusuf Hartono, Cor Kraaikamp, and Claire Merriman.

[8] Generalizations of Sturmian sequences associated with N-continued fraction algorithms 
 J. Number Theory 250 (2023), 49–83. , with  Lucía Rossi and Jörg M. Thuswaldner.

[7]  Intermediate β-shifts as greedy β-shifts with a hole 
Acta Math. Hung. 170, No. 1, 269-301 (2023), with  Tony Samuel.

[6] Alternating N-expansions.
Integers 22 (2022), Paper No. A65, 25 pp., with Karma Dajani.

[5] Tanaka-Ito alpha-continued fractions and matching.
Nonlinearity 34 (2021), no. 6, 3565–3582, with Carlo Carminati and Wolfgang Steiner.

[4] Matching for a family of infinite measure continued fraction transformations.
Discrete Contin. Dyn. Syst. 40 (2020), no. 11, 6309–6330, with Charlene Kalle, Marta Maggioni and Sara Munday.

[3] The beta-transformation with a hole at 0.
Ergodic Theory Dynam. Systems 40 (2020), no. 9, 2482–2514, with Charlene Kalle, Derong Kong and Wenxia Li.

[2] Invariant measures for continued fraction algorithms with finitely many digits.
J. Math. Anal. Appl. 454 (2017), no. 1, 106–126, with Cor Kraaikamp.

[1] Continued fraction expansions with variable numerators.
Ramanujan J. 37 (2015), no. 3, 617–639, with Karma Dajani and Cor Kraaikamp.

Preprints:
On Convergents of Proper continued Fractions.
With David Ralston.

Theses

PhD thesis: Matching, entropy, holes and expansions
Supervised by Charlene Kalle, promotor Frank den Hollander.

Master thesis: Finding infinitely many even or odd continued fractions by introducing a new family of maps
Supervised by Cor Kraaikamp.

Other

click here to see my fractal art (personal webpage in Dutch).

click here to see a manual to make a fractal scarf (collaboration with Anja Rueten-Budde).

Organising One World Numeration Seminar together with Shigeki Akiyama, Ayreena Bakhtawar, Karma Dajani, Kevin Hare, Hajime Kaneko, Lingmin Liao and Wolfgang Steiner.