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Etude ergodique de bêta-transformations aléatoires

Abstract : We work on the expansions of real numbers in non integer bases. We recall the construction of the natural extension of the greedy transformation introduced by Dajani, Kraaikamp and Solomyak. We then construct a geometrico-symbolic version of the natural extension of the random beta-transformation introduced by Dajani and Kraaikamp. This construction provides a new proof of the existence and uniqueness of an absolutely continuous invariant probability measure for the random beta-transformation, an expression for its density and the ergodicity of the random system. We then prove that this natural extension is a Bernoulli automorphism, generalising to the random case the result of Smorodinsky about the greedy transformation.
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https://theses.hal.science/tel-03516372
Contributor : Younès TIERCE Connect in order to contact the contributor
Submitted on : Tuesday, March 22, 2022 - 2:43:57 PM
Last modification on : Tuesday, March 29, 2022 - 3:58:37 AM

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  • HAL Id : tel-03516372, version 2

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Younes Tierce. Etude ergodique de bêta-transformations aléatoires. Systèmes dynamiques [math.DS]. Normandie Université, 2021. Français. ⟨NNT : 2021NORMR069⟩. ⟨tel-03516372v2⟩

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