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- W2949784857 abstract "Let $beta>1$ and let $m>be$ be an integer. Each $xin I_be:=[0,frac{m-1}{beta-1}]$ can be represented in the form [ x=sum_{k=1}^infty epsilon_kbeta^{-k}, ] where $epsilon_kin{0,1,...,m-1}$ for all $k$ (a $beta$-expansion of $x$). It is known that a.e. $xin I_beta$ has a continuum of distinct $beta$-expansions. In this paper we prove that if $beta$ is a Pisot number, then for a.e. $x$ this continuum has one and the same growth rate. We also link this rate to the Lebesgue-generic local dimension for the Bernoulli convolution parametrized by $beta$. When $beta<frac{1+sqrt5}2$, we show that the set of $beta$-expansions grows exponentially for every internal $x$." @default.
- W2949784857 created "2019-06-27" @default.
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- W2949784857 date "2009-02-03" @default.
- W2949784857 modified "2023-10-16" @default.
- W2949784857 title "Growth rate for beta-expansions" @default.
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- W2949784857 doi "https://doi.org/10.48550/arxiv.0902.0488" @default.
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