Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

A two-dimensional univoque set

100%

de Vrie M., Komornik V.

Fundamenta Mathematicae

2011

tom 212

nr 2

175-189

Let J ⊂ ℝ² be the set of couples (x,q) with q > 1 such that x has at least one representation of the form $x = ∑_{i=1}^{∞} c_{i} q^{-i}$ with integer coefficients $c_{i}$ satisfying $0 ≤ c_{i} < q$, i ≥ 1. In this case we say that $(c_{i}) = c₁c₂...$ is an expansion of x in base q. Let U be the set of couples (x,q) ∈ J such that x has exactly one expansion in base q. In this paper we deduce some topological and combinatorial properties of the set U. We characterize the closure of U, and we determine its Hausdorff dimension. For (x,q) ∈ J, we also prove new properties of the lexicographically largest expansion of x in base q.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Komornik V.

1 de Vrie M.

1 2011

Wyniki wyszukiwania

A two-dimensional univoque set