相关论文: Common dynamics of two Pisot substitutions with th…

Any infinite sequence of substitutions with the same matrix of the Pisot type defines a symbolic dynamical system which is minimal. We prove that, to any such sequence, we can associate a compact set (Rauzy fractal) by projection of the…

In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is reflection through the origin. Given an unimodular irreducible Pisot substitution, we consider the…

We define a generic algorithmic framework to prove pure discrete spectrum for the substitutive symbolic dynamical systems associated with some infinite families of Pisot substitutions. We focus on the families obtained as finite products of…

Let $\sigma$ be a non-unit Pisot substitution and let $\alpha$ be the associated Pisot number. It is known that one can associate certain fractal tiles, so-called \emph{Rauzy fractals}, with $\sigma$. In our setting, these fractals are…

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…

We provide a proof for one version of Pisot conjecture. We make use of the weak mixing property of the subshift of finite type derived from the prefix-suffix automaton to conclude that the substitution dynamical system has pure discrete…

We prove an extension of the well-known Pisot substitution conjecture to the $S$-adic symbolic setting on two letters. The proof relies on the use of Rauzy fractals and on the fact that strong coincidences hold in this framework.

We provide a proof of Pisot conjecture, a classification problem in Ergodic Theory on recurrent sequences generated by irreducible Pisot substitutions.

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…

In this article, we prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an…

We consider the structure of Pisot substitution tiling spaces, in particular, the structure of those spaces for which the translation action does not have pure discrete spectrum. Such a space is always a measurable m-to-one cover of an…

We give a sufficient geometric condition for a subshift to be measurably isomorphic to a domain exchange and to a translation on a torus. And for an irreducible unit Pisot substitution, we introduce a new topology on the discrete line and…

We propose to consider a mutual incidence matrix $M$ of two balanced incomplete block designs built on the same finite set. In the simplest case, this matrix reduces to the standard incidence matrix of one block design. We find all…

In this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of Pisot type. Central sets, first introduced by Furstenberg using notions from…

Generalized abelian equivalence compares words by their factors up to a certain bounded length. The associated complexity function counts the equivalence classes for factors of a given size of an infinite sequence. How practical is this…

We compute the Poisson bracket relations for the monodromy matrix of the auxiliary linear problem. If the basic Poisson bracket relations of the model contain derivatives, this computation leads to a peculiar type of symmetry breaking which…

We present a combinatorial approach to rigorously show the existence of fixed points, periodic orbits, and symbolic dynamics in discrete-time dynamical systems, as well as to find numerical approximations of such objects. Our approach…

This paper shows that the resolvent algebra $\mathcal{R}\left( \mathbb{R}^2,\sigma \right)$ can accommodate dynamics induced by self-adjoint Hamiltonians on $L^2\left( \mathbb{R} \right)$ describing a single non-relativistic spinless…

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…

Sellami and Sirvent conjectured that the balanced pair algorithm fails for the following pair of Pisot substitutions: \[ \varphi_0: \begin{array}{l} a \mapsto abc b \mapsto a c \mapsto ac \end{array} \quad \text{ and } \quad \varphi_1:…