Charlene Kalle

Beta-expansions, natural extensions and multiple tilings associated with Pisot units

From the works of Rauzy and Thurston, we know how to construct (multiple) tilings of some Euclidean space using the conjugates of a Pisot unit

Isomorphisms between positive and negative -transformations

\beta

Random ß-expansions with deleted digits

and the greedy

Transformations Generating Negative [Beta]-expansions

\beta

A natural extension for the greedy β-transformation with three arbitrary digits

-transformation. In this paper, we consider different transformations generating expansions in base~

Beta-expansions, natural extensions and multiple tilings

\beta

Local dimensions for the random β-transformation

, including cases where the associated subshift is not sofic. Under certain mild conditions, we show that they give multiple tilings. We also give a necessary and sufficient condition for the tiling property, generalizing the weak finiteness property (W) for greedy

Invariant measures, matching and the frequency of 0 for signed binary expansions.

\beta

A natural extension for the greedy -transformation with three arbitrary digits

-expansions. Remarkably, the symmetric

The random continued fraction transformation

\beta