ON SELF-SIMILARITIES OF CUT-AND-PROJECT SETS
dc.contributor.author | Masáková , Zuzana | |
dc.contributor.author | Mazáč , Jan | |
dc.date.accessioned | 2018-01-18T08:11:22Z | |
dc.date.available | 2018-01-18T08:11:22Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Acta Polytechnica. 2017, vol. 57, no. 6, p. 430-445. | |
dc.identifier.issn | 1210-2709 (print) | |
dc.identifier.issn | 1805-2363 (online) | |
dc.identifier.uri | http://hdl.handle.net/10467/73719 | |
dc.description.abstract | Among the commonly used mathematical models of quasicrystals are Delone sets constructed using a cut-and-project scheme, the so-called cut-and-project sets. A cut-and-project scheme (L,π1, π2) is given by a lattice L in Rs and projections π1, π2 to suitable subspaces V1, V2. In this paper we derive several statements describing the connection between self-similarity transformations of the lattice L and transformations of its projections π1(L), π2(L). For a self-similarity of a set Σ we take any linear mapping A such that AΣ ⊂ Σ, which generalizes the notion of self-similarity usually restricted to scaled rotations. We describe a method of construction of cut-and-project scheme such that π1(L) ⊂ R2 is invariant under an isometry of order 5. We describe all linear self-similarities of the scheme thus constructed and show that they form an 8-dimensional associative algebra over the ring Z. We perform an example of a cut-and-project set with linear self-similarity which is not a scaled rotation. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | České vysoké učení technické v Praze | cs |
dc.publisher | Czech Technical University in Prague | en |
dc.relation.ispartofseries | Acta Polytechnica | |
dc.relation.uri | https://ojs.cvut.cz/ojs/index.php/ap/article/view/4587 | |
dc.rights | Creative Commons Attribution 4.0 International License | en |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | self-similarity | en |
dc.subject | quasicrystal | en |
dc.subject | cut-and-project scheme | en |
dc.title | ON SELF-SIMILARITIES OF CUT-AND-PROJECT SETS | |
dc.type | article | en |
dc.date.updated | 2018-01-18T08:11:22Z | |
dc.identifier.doi | 10.14311/AP.2017.57.0430 | |
dc.rights.access | openAccess | |
dc.type.status | Peer-reviewed | |
dc.type.version | publishedVersion |
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