相关论文: Connectedness of fractals associated with Arnoux-R…

We construct geometric realizations for the infimax family of substitutions by generalizing the Rauzy-Canterini-Siegel method for a single substitution to the S-adic case. The composition of each countably infinite subcollection of…

This paper uses a connection between bounded remainder sets in $\mathbb{R}^d$ and cut-and-project sets in $\mathbb{R}$ together with the fact that each one-dimensional Pisot substitution sequence is bounded distance equivalent to some…

The Rauzy gasket is the attractor of a parabolic, nonconformal iterated function system on the projective plane which describes an exceptional parameter set in various important topological and dynamical problems. Since 2009 there have been…

We associate, with every infinite word over a finite alphabet, an increasing sequence of rooted finite graphs, which provide a discrete approximation of the famous Sierpi\'nski carpet fractal. Each of these sequences converges, in the…

In this paper, we study arithmetical and topological properties for a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we prove the number of neighbors of…

In the present article, we deal with geometrical objects induced by the tent maps associated with special Pisot numbers that we call tent-tiles. They are compact subsets of the one-, two-, or three-dimensional Euclidean space, depending on…

Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example (the Rauzy dynamics) concerns an action on permutations, associated to interval exchange transformations (IET) for the…

Crisp and $L$-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or $L$-fuzzy) ambiguous…

Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly…

In this paper, we settle a long-standing problem on the connectivity of spaces of finite unit norm tight frames (FUNTFs), essentially affirming a conjecture first appearing in [Dykema and Strawn, 2003]. Our central technique involves…

We prove that any unimodular Pisot substitution subshift is measurably conjugate to a domain exchange in an Euclidean space which is a finite topological extension of a translation on a torus.This generalizes the pioneer works of Rauzy and…

We introduce the concept of F-decomposable systems, well-ordered inverse systems of Hausdorff compacta with fully closed bonding mappings. A continuous mapping between Hausdorff compacta is called fully closed if the intersection of the…

The fragmentation processes of exchangeable partitions have already been studied by several authors. In this paper, we examine rather fragmentation of exchangeable compositions, that means partitions of $\mathbb{N}$ where the order of the…

In this paper we study various fractal geometric aspects of the Minkowski question mark function $Q.$ We show that the unit interval can be written as the union of the three sets $\Lambda_{0}:=\{x:Q'(x)=0\}$,…

The concept of fractal index is introduced in connection with the idea of universal class $h$ of particles or quasiparticles, termed fractons, which obey fractal statistics. We show the relation between fractons and conformal field…

In this paper, we study the fractal properties of the boundary of the Cantorval connected with Guthrie-Nymann's series. In particular, we prove that such a Cantorval can be represented as a union of open intervals and a Cantor set having…

This paper studies geometric and spectral properties of $S$-adic shifts and their relation to continued fraction algorithms. These shifts are symbolic dynamical systems obtained by iterating infinitely many substitutions. Pure discrete…

We explore the problem of finding the Hausdorff dimension of the set of points that recur to shrinking targets on a self-affine fractal. To be exact, we study the dimension of a certain related symbolic recurrence set. In many cases this…

We relate various concepts of fractal dimension of the limiting set C in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in C (the "dust"). In two dimensions, we…

The averaged distance structure of one-dimensional regular model sets is determined via their pair correlation functions. The latter lead to covariograms and cross covariograms of the windows, which give continuous functions in internal…