Jörg M. Thuswaldner

activity

20142025

collaborators

7 papers

math.MG2025

Neighbors of self-affine tiles and Rauzy Fractals

Benoît Loridant, Jörg M. Thuswaldner, Shu-Qin Zhang

Although the theory of self-affine tiles and the theory of Rauzy fractals are quite different from each other, they have some common features. Both, self-affine tiles and Rauzy fra…

math.NT2025

Addition Automata and Attractors of Digit Systems Corresponding to Expanding Rational Matrices

Anjelo Gabriel R. Cruz, Manuel Joseph C. Loquias, Jörg M. Thuswaldner

Let $A$ be an expanding $2 \times 2$ matrix with rational entries and $Z^{2} [A]$ be the smallest $A$ -invariant $Z$ -module containing $Z^{2}$ . Let $\mathcal{D…

math.NT2024

A finiteness condition for complex continued fraction algorithms

Charlene Kalle, Fanni M. Sélley, Jörg M. Thuswaldner

It is desirable that a given continued fraction algorithm is simple in the sense that the possible representations can be characterized in an easy way. In this context the so-calle…

math.GT2021

On self-affine tiles that are homeomorphic to a ball

Jörg M. Thuswaldner, Shu-Qin Zhang

Let $M$ be a $3 \times 3$ integer matrix which is expanding in the sense that each of its eigenvalues is greater than $1$ in modulus and let $D \subset Z^{3}$ be a…

math.GT2018

On self-affine tiles whose boundary is a sphere

Jörg Thuswaldner, Shu-qin Zhang

Let $M$ be a $3 \times 3$ integer matrix each of whose eigenvalues is greater than $1$ in modulus and let $D \subset Z^{3}$ be a set with $∣ D ∣ = ∣ det M ∣$ , ca…

math.NT2018

Number systems over general orders

Jan-Hendrik Evertse, Kálmán Győry, Attila Pethő +1

Let $O$ be an order, that is a commutative ring with $1$ whose additive structure is a free $Z$ -module of finite rank. A generalized number system (GNS for short…

math.GN2014

On cut sets of attractors of iterated function systems

Benoît Loridant, Jun Luo, Tarek Sellami +1

In this paper, we study cut sets of attractors of iteration function systems (IFS) in $R^{d}$ . Under natural conditions, we show that all irreducible cut sets of these attra…