相关论文: On substitution tilings and Delone sets without fi…

We investigate the dynamics of substitution subshifts and their associated tiling spaces. For a given subshift, the associated tiling spaces are all homeomorphic, but their dynamical properties may differ. We give criteria for such a tiling…

The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…

We give explicit $C^1$-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with…

A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can be enforced by finitely many local…

We formulate and prove a variational principle (in the sense of thermodynamics) for random domino tilings, or equivalently for the dimer model on a square grid. This principle states that a typical tiling of an arbitrary finite region can…

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…

We prove that in every compact space of Delone sets in $\mathbb{R}^d$ which is minimal with respect to the action by translations, either all Delone sets are uniformly spread, or continuously many distinct bounded displacement equivalence…

We consider infinite measure-preserving non-primitive self-similar tiling systems in Euclidean space $\mathbb R^d$. We establish the second-order ergodic theorem for such systems, with exponent equal to the Hausdorff dimension of a…

We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving 3 tiles which sample the tiling sets {\em via} Monte Carlo Markov chains. We determine…

We study electronic properties as a function of the six types of local environments found in the octagonal tiling. The density of states has six characteristic forms, although the detailed structure differs from site to site since no two…

Overlap coincidence is an equivalent criterion to pure discrete spectrum of the dynamics of self affine tilings. In the case of one dimension, strong coincidence on m letter irreducible substitution has been introduced in Dekking (1978) and…

The periodic tiling conjecture asserts that if a region $\Sigma\subset \mathbb R^d$ tiles $\mathbb R^d$ by translations then it admits at least one fully periodic tiling. This conjecture is known to hold in $\mathbb R$, and recently it was…

We introduce a functor which associates to every measure preserving system (X,B,\mu,T) a topological system (C_2(\mu),\tilde{T}) defined on the space of 2-fold couplings of \mu, called the topological lens of T. We show that often the…

We consider close-packed tiling models of geometric objects -- a mixture of hardcore dimers and plaquettes -- as a generalisation of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be…

Let $(X, T)$ be a topological dynamical system. We show that if each invariant measure of $(X, T)$ gives rise to a measure-theoretic dynamical system that is either: a. rigid along a sequence of "bounded prime volume" or b. admits a…

We introduce a counterpart to the notion of vertex disjoint tilings by copy of a fixed graph F to the setting of graphons. The case F=K_2 gives the notion of matchings in graphons. We give a transference statement that allows us to switch…

The purpose of this article is to establish theories concerning $p$-adic analogues of Hodge cohomology and Deligne-Beilinson cohomology with coefficients in variations of mixed Hodge structures. We first study log overconvergent…

Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger…

Given a finite set ${S_1...,S_k}$ of substitution maps acting on a certain finite number (up to translations) of tiles in $\rd$, we consider the multi-substitution tiling space associated to each sequence $\bar a\in {1,...,k}^{\mathbb{N}}$.…

We study the structure of invariant measures for continuous automorphisms of compact metrizable abelian groups satisfying the descending chain condition. We show that the finitely supported invariant measures are weak-* dense in the space…