Leiden University Student Repository

Dijk, S. van (4509)

Fractal dimensions of restricted digit sets for random Lüroth expansions

Master thesis | Mathematics (MSc)

In this thesis we study restricted digit sets for random L¨uroth expansions, a type of number expansion for numbers in the unit interval generalising the L¨uroth expansions introduced in [L¨ur83]. By studying a random transformation that generates these expansions and a corresponding iterated function system we find a general formula describing the Hausdorff dimensions of all of these restricted digit sets. We then study a family of two-dimensional fractal sets induced by the skew product representation of this random transformation. In particular, we find conditions under which the box-counting dimension of such a fractal equals the corresponding affinity dimension and use this to find upper and lower bounds.

Author

Dijk, S. van

Faculty

Faculty of Science

Supervisors

Kalle, C.C.C.J.

ECTS Credits

40

Language

en