A natural extension for the greedy beta-transformation with three deleted digits

Mathematics – Dynamical Systems

Scientific paper

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21 pages

Scientific paper

We give an explicit expression for the invariant measure, absolutely
continuous with respect to the Lebesgue measure, of the greedy
beta-transformation with three deleted digits. We define a version of the
natural extension of the transformation to obtain this expression. We get that
the transformation is exact and weakly Bernoulli.

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