View More View Less
  • 1 Utrecht University Department of Mathematics Postbus 80.000 3508 TA Utrecht the Netherlands
Restricted access

Abstract  

We construct a planar version of the natural extension of the piecewise linear transformation T generating greedy β-expansions with digits in an arbitrary set of real numbers A = {a 0, a 1, a 2}. As a result, we derive in an easy way a closed formula for the density of the unique T-invariant measure µ absolutely continuous with respect to Lebesgue measure. Furthermore, we show that T is exact and weak Bernoulli with respect to µ.

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Jan 2021 0 0 0
Feb 2021 0 0 0
Mar 2021 0 0 0
Apr 2021 0 0 0
May 2021 0 0 0
Jun 2021 0 0 0
Jul 2021 0 0 0