Abstract
We construct a Lebesgue measure preserving natural extension of a skew product system related to the random β-transformation Kβ. This allows us to give a formula for the density of the absolutely continuous invariant probability
measure of Kβ, answering a question of Dajani and de Vries, and also to evaluate some estimates on the typical branching rate of the set of β-expansions of a real number.
measure of Kβ, answering a question of Dajani and de Vries, and also to evaluate some estimates on the typical branching rate of the set of β-expansions of a real number.
| Original language | English |
|---|---|
| Pages (from-to) | 403-419 |
| Number of pages | 17 |
| Journal | Acta Mathematica Hungarica |
| Volume | 142 |
| Issue number | 2 |
| Early online date | 11 Dec 2011 |
| DOIs | |
| Publication status | Published - 2014 |