## Développement en base $$\theta$$ , répartition modulo un de la suite $$(x\theta ^ n)$$, n$$\geq 0$$, langages codes et $$\theta$$-shift. (Expansion in base $$\theta$$ , uniform distribution of the sequence $$(x\theta ^ n)$$, n$$\geq 0$$, coding languages and $$\theta$$-shift).(French)Zbl 0628.58024

A $$\theta$$ shift is a subshift defined by a real number greater than one. The arithmetic properties of $$\theta$$ and the dynamical properties of the subshifts are closely related. A coded system is another type of subshift, these are defined from the point of view of coding theory. In this paper it is shown that every $$\theta$$ shift is a coded system. If $$\theta$$ is a Pisot number of degree s, it is shown that there is a toral automorphism of the s-torus which is a continuous factor of the $$\theta$$ shift.
Reviewer: B.Kitchens

### MSC:

 37A99 Ergodic theory 11K06 General theory of distribution modulo $$1$$ 28D99 Measure-theoretic ergodic theory 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
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### References:

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