Let α be a root of an irreducible quadratic polynomial x2+ Ax+ B with integer coefficients A, B
and assume that α forms a canonical number system, ie, each x∈ ℤ [α] admits a …

In this paper we study properties of the fundamental domain [Fscr] β of number systems,
which are defined in rings of integers of number fields. First we construct addition automata …

Pour une matrice réelle M d'ordre 2 donnée, on peut définir la notion de représentation M-
adique d'un élément de ℝ 2. On note ℱ le domaine fondamental constitué des nombres de …

Let T be a tile of a self-affine lattice tiling. We give an algorithm that allows to determine all
neighbours of T in the tiling. This can be used to characterize the sets VL of points, where T …

A standard way to parametrize the boundary of a connected fractal tile T is proposed. The
parametrization is Hölder continuous from R/Z to∂ T and fixed points of∂ T have algebraic …

NATURAL TILING, LATTICE TILING AND LEBESGUE MEASURE OF INTEGRAL SELF-AFFINE
TILES Page 1 J. London Math. Soc. (2) 74 (2006) 184–204 Cо2006 London Mathematical …

On the boundary connectedness of connected tiles Page 1 Math. Proc. Camb. Phil. Soc. (2004),
137, 397 c© 2004 Cambridge Philosophical Society DOI: 10.1017/S0305004104007625 …

A monic polynomial f (x) ∈\mathbb Z x is said to have the height reducing property (HRP) if
there exists a polynomial h (x) ∈\mathbb Z x such that f (x) h (x)= a_n x^ n+ a_ n-1 x^ n-1+ …

The Twin Dragon and Rauzy fractals are intersected with the real axis. In the Twin Dragon
case, unexpectedly from its fractal nature, the intersection is an interval characterized by a …

We consider the asymptotic behavior of b-additive functions f with respect to a base b of a
canonical number system in the Gaussian number field. In particular, we get a normal limit …