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

Bertrand-Mathis, Anne

Bull. Soc. Math. Fr. 114, 271-323 (1986).

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

Keywords:

\(\theta \) shift; coded system; Pisot number; toral automorphism

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