Beta-Expansions for Cubic Pisot Numbers

  title={Beta-Expansions for Cubic Pisot Numbers},
  author={Fr{\'e}d{\'e}rique Bassino},
Real numbers can be represented in an arbitrary base β > 1 using the transformation Tβ : x → βx (mod 1) of the unit interval; any real number x ∈ [0, 1] is then expanded into dβ(x) = (xi)i≥1 where xi = βT i−1 β (x) . The closure of the set of the expansions of real numbers of [0, 1[ is a subshift of {a ∈ N | a < β}N, called the beta-shift. This dynamical system is characterized by the beta-expansion of 1; in particular, it is of finite type if and only if dβ(1) is finite; β is then called a… CONTINUE READING