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pro vyhledávání: '"THUSWALDNER, Jörg"'
We study {\it permeable} sets. These are sets \(\Theta \subset \mathbb{R}^d\) which have the property that each two points \(x,y\in \mathbb{R}^d\) can be connected by a short path \(\gamma\) which has small (or even empty, apart from the end points o
Externí odkaz:
http://arxiv.org/abs/2410.17254
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-called finite range condition plays a prominent role. We show that this con
Externí odkaz:
http://arxiv.org/abs/2406.18689
Given a positive integer $N$ and $x$ irrational between zero and one, an $N$-continued fraction expansion of $x$ is defined analogously to the classical continued fraction expansion, but with the numerators being all equal to $N$. Inspired by Sturmia
Externí odkaz:
http://arxiv.org/abs/2209.00978
We consider digit systems $(A,\mathcal{D})$, where $ A \in \mathbb{Q}^{n\times n}$ is an expanding matrix and the digit set $\mathcal{D}$ is a suitable subset of $\mathbb{Q}^n$. To such a system, we associate a self-affine set $\mathcal{F} = \mathcal
Externí odkaz:
http://arxiv.org/abs/2110.09112
Let $A$ be a $d \times d$ matrix with rational entries which has no eigenvalue $\lambda \in \mathbb{C}$ of absolute value $|\lambda| < 1$ and let $\mathbb{Z}^d[A]$ be the smallest nontrivial $A$-invariant $\mathbb{Z}$-module. We lay down a theoretica
Externí odkaz:
http://arxiv.org/abs/2107.14168
Autor:
Thuswaldner, Jörg M., Zhang, Shu-Qin
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 $\mathcal{D} \subset \mathbb{Z}^3$ be a digit set containing $|\det M|$ elements. Then the unique nonempty com
Externí odkaz:
http://arxiv.org/abs/2107.12076
We estimate Weyl sums over the integers with sum of binary digits either fixed or restricted by some congruence condition. In our proofs we use ideas that go back to a paper by Banks, Conflitti and the first author (2002). Moreover, we apply the "mai
Externí odkaz:
http://arxiv.org/abs/2105.04835
Autor:
Rossi, Lucía, Thuswaldner, Jörg M.
In the present paper we explore a way to represent numbers with respect to the base $-\frac32$ using the set of digits $\{0,1,2\}$. Although this number system shares several properties with the classical decimal system, it shows remarkable differenc
Externí odkaz:
http://arxiv.org/abs/2102.11106
For two distinct integers $m_1,m_2\ge2$, we set $\alpha_1=[0;\overline{1,m_1}]$ and $\alpha_2=[0;\overline{1,m_2}]$ and we denote by $S_{\alpha_1}(n)$ and $S_{\alpha_2}(n)$ respectively the sum of digits functions in the Ostrowski $\alpha_1$ and $\al
Externí odkaz:
http://arxiv.org/abs/2006.06960
It has been a long standing problem to find good symbolic codings for translations on the $d$-dimensional torus that enjoy the beautiful properties of Sturmian sequences like low factor complexity and good local discrepancy properties. Inspired by Ra
Externí odkaz:
http://arxiv.org/abs/2005.13038