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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2014

Non-normal numbers in dynamical systems fulfilling the specification property

Manfred G. Madritsch
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Izabela Petrykiewicz
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Résumé

In the present paper we want to focus on this dichotomy of the non-normal numbers -- on the one hand they are a set of measure zero and on the other hand they are residual -- for dynamical system fulfilling the specification property. These dynamical systems are motivated by $\beta$-expansions. We consider the limiting frequencies of digits in the words of the languagse arising from these dynamical systems, and show that not only a typical $x$ in the sense of Baire is non-normal, but also its Cesáro variants diverge.

Dates et versions

hal-00959286 , version 1 (14-03-2014)

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Manfred G. Madritsch, Izabela Petrykiewicz. Non-normal numbers in dynamical systems fulfilling the specification property. Discrete and Continuous Dynamical Systems - Series A, 2014, 34 (11), pp.4751 - 4764. ⟨10.3934/dcds.2014.34.4751⟩. ⟨hal-00959286⟩
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