Extensions of the random beta-transformation

Younès Tierce (Université de Rouen Normandie)

09-Nov-2021, 14:00-14:30 (2 years ago)

Abstract: Let $\beta \in (1,2)$ and $I_\beta := [0,\frac{1}{\beta-1}]$. Almost every real number of $I_\beta$ has infinitely many expansions in base $\beta$, and the random $\beta$-transformation generates all these expansions. We present the construction of a "geometrico-symbolic" extension of the random $\beta$-transformation, providing a new proof of the existence and unicity of an absolutely continuous invariant probability measure, and an expression of the density of this measure. This extension shows off some nice renewal times, and we use these to prove that the natural extension of the system is a Bernoulli automorphism.

dynamical systemsnumber theory

Audience: researchers in the topic

( slides )


One World Numeration seminar

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