On the average growth exponent for beta-expansions

2008/08/11 by Sidorov, Nikita
#11A63 #28D05 #42A85 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0808.1589

Abstract

Let \be∈(1,2). Each x∈ I_\be:=[0,(1)/(\be-1)] can be represented in the form x=∑_k=1^∞ a_k\be^-k, where a_k∈\0,1\ for all k (a \be-expansion of x). It was shown in \citeS that a.e. x∈ I_\be has a continuum of distinct \be-expansions. In this paper we show that for a generic x, this continuum has one and the same growth rate, i.e., the general \be-expansions exhibit an ergodic behaviour. When \be

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