Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Loridant, Benoit"'
The Knuth Twin Dragon is a compact subset of the plane with fractal boundary of Hausdorff dimension $s = (\log \lambda)/(\log \sqrt{2})$, $\lambda^3 = \lambda^2 + 2$. Although the intersection with a generic line has Hausdorff dimension $s-1$, we pro
Externí odkaz:
http://arxiv.org/abs/2402.18371
We consider the self-affine tiles with collinear digit set defined as follows. Let $A,B\in\mathbb{Z}$ satisfy $|A|\leq B\geq 2$ and $M\in\mathbb{Z}^{2\times2}$ be an integral matrix with characteristic polynomial $x^2+Ax+B$. Moreover, let $\mathcal{D
Externí odkaz:
http://arxiv.org/abs/1801.02957
A Peano continuum means a locally connected continuum. A compact metric space is called a \emph{Peano compactum} if all its components are Peano continua and if for any constant $C>0$ all but finitely many of its components are of diameter less than
Externí odkaz:
http://arxiv.org/abs/1712.06300
Autor:
Loridant, Benoît, Luo, Jun
We describe non-locally connected planar continua via the concepts of fiber and numerical scale. Given a continuum $X\subset\mathbb{C}$ and $x\in\partial X$, we show that the set of points $y\in \partial X$ that cannot be separated from $x$ by any fi
Externí odkaz:
http://arxiv.org/abs/1703.05914
Autor:
Loridant, Benoit, Minervino, Milton
We set up a geometrical theory for the study of the dynamics of reducible Pisot substitutions. It is based on certain Rauzy fractals generated by duals of higher dimensional extensions of substitutions. We obtain under certain hypotheses geometric re
Externí odkaz:
http://arxiv.org/abs/1612.08373
Autor:
Loridant, Benoît, Zhang, Shu-qin
We study the topological properties of a class of planar crystallographic replication tiles. Let $M\in\mathbb{Z}^{2\times2}$ be an expanding matrix with characteristic polynomial $x^2+Ax+B$ ($A,B\in\mathbb{Z}$, $B\geq 2$) and ${\bf v}\in\mathbb{Z}^2$
Externí odkaz:
http://arxiv.org/abs/1611.04903
In this paper, we study cut sets of attractors of iteration function systems (IFS) in $\mathbb{R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a criterion for
Externí odkaz:
http://arxiv.org/abs/1412.1975
Autor:
Loridant, Benoît
We consider the substitution $\sigma_{a,b}$ defined by $$\begin{array}{rlcl} \sigma_{a,b}: & 1 & \mapsto & \underbrace{1\ldots 1}_{a}2 \\ & 2 & \mapsto & \underbrace{1\ldots 1}_{b}3 \\ & 3 & \mapsto & 1 \end{array} $$ with $a\geq b\geq 1$. The shift
Externí odkaz:
http://arxiv.org/abs/1411.7544
Publikováno v:
Topology and its Applications 202 (2016), no. 1, 21-39
We introduce a numerical scale to quantify to which extent a planar continuum is not locally connected. For a locally connected continuum, the numerical scale is zero; for a continuum like the topologist's sine curve, the scale is one; for an indecom
Externí odkaz:
http://arxiv.org/abs/1411.6776
Publikováno v:
Journal of Fractal Geometry 1 (2014), no. 4, 427-447
We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. This characterizes all countable fundamental groups for planar Rauzy frac
Externí odkaz:
http://arxiv.org/abs/1312.7829