Linearly repetitive Delone sets are rectifiable
| Autor: | Daniel Coronel, J.-M. Gambaudo, José Aliste-Prieto |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Discrete mathematics
Mathematics::Dynamical Systems Applied Mathematics Substitution tiling Lattice (group) Integer lattice Substitution (algebra) FOS: Physical sciences Metric Geometry (math.MG) Delone set Dynamical Systems (math.DS) Mathematical Physics (math-ph) Substitution matrix Homeomorphism Combinatorics Mathematics - Metric Geometry Bounded function FOS: Mathematics Mathematics::Metric Geometry Mathematics - Dynamical Systems Mathematical Physics Analysis Mathematics |
| Zdroj: | ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE Artículos CONICYT CONICYT Chile instacron:CONICYT Analysis & Pde |
| DOI: | 10.48550/arxiv.1103.5423 |
| Popis: | We show that every linearly repetitive Delone set in the Euclidean d-space R d , with d ⩾ 2 , is equivalent, up to a bi-Lipschitz homeomorphism, to the integer lattice Z d . In the particular case when the Delone set X in R d comes from a primitive substitution tiling of R d , we give a condition on the eigenvalues of the substitution matrix which ensures the existence of a homeomorphism with bounded displacement from X to the lattice β Z d for some positive β. This condition includes primitive Pisot substitution tilings but also concerns a much broader set of substitution tilings. |
| Databáze: | OpenAIRE |
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