Conjugacies of model sets
| Autor: | Lorenzo Sadun, Johannes Kellendonk |
|---|---|
| Přispěvatelé: | Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics and Statistics [Texas Tech], Texas Tech University [Lubbock] (TTU) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
37B50
Dimension (graph theory) [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Dynamical Systems (math.DS) Disjoint sets Delone set 01 natural sciences Combinatorics FOS: Mathematics Discrete Mathematics and Combinatorics 37B50 52C22 Mathematics - Dynamical Systems 0101 mathematics Mathematics Discrete mathematics Finite group Group (mathematics) Applied Mathematics 010102 general mathematics Dynamical Systems 010101 applied mathematics Projection (relational algebra) Tilings Product (mathematics) Topological conjugacy Analysis |
| Zdroj: | 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⟩ |
| ISSN: | 1078-0947 |
| DOI: | 10.3934/dcds.2017161⟩ |
| Popis: | 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 is topologically conjugate to $M$ is mutually locally derivable (MLD) to a model set $M'$ that has the same internal group and window as $M$, but has a different projection from $H \times R^d$ to $R^d$. In cohomological terms, this means that the group $H^1_{an}(M,R)$ of asymptotically negligible classes has dimension $n$. We also exhibit a counterexample when the second hypothesis is removed, constructing two topologically conjugate FLC Delone sets, one a model set and the other not even a Meyer set. Updated to the published version |
| Databáze: | OpenAIRE |
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