Tilings and traces

Autor: Treviño, Rodrigo

This paper deals with (globally) random substitutions on a finite set of prototiles. Using renormalization tools applied to objects from operator algebras we establish upper and lower bounds on the rate of deviations of ergodic averages for the uniqu

Externí odkaz: http://arxiv.org/abs/1906.00466

Equicontinuous factors, proximality and Ellis semigroup for Delone sets

Autor: Aujogue, Jean-baptiste, Barge, Marcy, Kellendonk, Johannes, Lenz, Daniel

We discuss the application of various concepts from the theory of topological dynamical systems to Delone sets and tilings. We consider in particular, the maximal equicontinuous factor of a Delone dynamical system, the proximality relation and the en

Externí odkaz: http://arxiv.org/abs/1407.1787

Spectral triples and aperiodic order

Autor: Kellendonk, J., Savinien, J.

We construct spectral triples for compact metric spaces (X, d). This provides us with a new metric d_s on X. We study its relation with the original metric d. When X is a subshift space, or a discrete tiling space, and d satisfies certain bounds we a

Externí odkaz: http://arxiv.org/abs/1010.0156

Tiling groupoids and Bratteli diagrams

Autor: Bellissard, J., Julien, A., Savinien, J.

Let T be an aperiodic and repetitive tiling of R^d with finite local complexity. Let O be its tiling space with canonical transversal X. The tiling equivalence relation R_X is the set of pairs of tilings in X which are translates of each others, with

Externí odkaz: http://arxiv.org/abs/0911.0080

Conjugacies of model sets

Autor: Lorenzo Sadun, Johannes Kellendonk

Publikováno v: Discrete and Continuous Dynamical Systems-Series A
Discrete and Continuous Dynamical Systems-Series A, American Institute of Mathematical Sciences, 2017, 37 (7), pp.3805-3830. ⟨10.3934/dcds.2017161⟩

Let $M$ be a model set meeting two simple conditions: (1) the internal space $H$ is a product of $R^n$ and a finite group, and (2) the window $W$ is a finite union of disjoint polyhedra. Then any point pattern with finite local complexity (FLC) that

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::39d50ef4f91f7c7336c590136c7ba48b
https://hal.archives-ouvertes.fr/hal-01006289/file/Mixed16.pdf