Complexity of non-abelian cut-and-project sets of polytopal type I: special homogeneous Lie groups
Kaiser, Peter
1
1 Institut für Algebra und Geometrie (IAG), Karlsruher Institut für Technologie (KIT)
11 Institut für Algebra und Geometrie (IAG), Karlsruher Institut für Technologie (KIT)
Abstract:
The aim of this paper is to determine the asymptotic growth rate of the complexity function of cut-and-project sets in the non-abelian case. In the case of model sets of polytopal type in homogeneous two-step nilpotent Lie groups, we can establish that the complexity function asymptotically behaves like $r^{homdim(G)dim(H)}$. Further, we generalize the concept of acceptance domains to locally compact second countable groups.
| Zugehörige Institution(en) am KIT | Institut für Algebra und Geometrie (IAG) |
| Publikationstyp | Zeitschriftenaufsatz |
| Publikationsjahr | 2024 |
| Sprache | Englisch |
| Identifikator | ISSN: 0143-3857, 1469-4417 KITopen-ID: 1000171063 |
| Erschienen in | Ergodic Theory and Dynamical Systems |
| Verlag | Cambridge University Press (CUP) |
| Seiten | 1–43 |
| Vorab online veröffentlicht am | 13.05.2024 |
| Schlagwörter | cut-and-project sets, complexity, model sets, aperiodic order, Lie group |
| Nachgewiesen in | Dimensions Web of Science Scopus |