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Pré-Publication, Document De Travail Année : 2019

Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series

Résumé

Let $f : [0,1)\rightarrow [0,1)$ be a $2$-interval piecewise affine increasing map which is injective but not surjective. Such a map $f$ has a rotation number and can be parametrized by three real numbers. We make fully explicit the dynamics of $f$ thanks to two specific functions $\delta$ and $\phi$ depending on these parameters whose definitions involve Hecke-Mahler series. As an application, we show that the rotation number of $f$ is rational, when the three parameters are algebraic numbers.

Dates et versions

hal-02281905 , version 1 (09-09-2019)

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Michel Laurent, Arnaldo Nogueira. Dynamics of 2-interval piecewise affine maps and Hecke-Mahler series. 2019. ⟨hal-02281905⟩
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