# American Institute of Mathematical Sciences

January  2007, 18(1): 199-217. doi: 10.3934/dcds.2007.18.199

## Random β-expansions with deleted digits

 1 Department of Mathematics, Utrecht University, Postbus 80.000, 3508 TA Utrecht, Netherlands, Netherlands

Received  June 2006 Revised  November 2006 Published  February 2007

In this paper we define random $\beta$-expansions with digits taken from a given set of real numbers $A= \{ a_1 , \ldots , a_m \}$. We study a generalization of the greedy and lazy expansion and define a function $K$ that generates essentially all $\beta$-expansions with digits belonging to the set $A$. We show that $K$ admits an invariant measure $\nu$ under which $K$ is isomorphic to the uniform Bernoulli shift on $A$.
Citation: Karma Dajani, Charlene Kalle. Random β-expansions with deleted digits. Discrete & Continuous Dynamical Systems - A, 2007, 18 (1) : 199-217. doi: 10.3934/dcds.2007.18.199
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