Substitution Tilings and Separated Nets with Similarities to the Integer Lattice
| dc.creator | Solomon, Yaar | |
| dc.date | 2008-10-29 | |
| dc.date | 2009-01-18 | |
| dc.date.accessioned | 2026-07-07T12:30:47Z | |
| dc.date.available | 2026-07-07T12:30:47Z | |
| dc.description | We show that any primitive substitution tiling of the plane creates a separated net which is biLipschitz to the integer lattice. Then we show that if H is a primitive Pisot substitution in an Euclidean space, for every separated net Y, that corresponds to some tiling of the tiling space, there exists a bijection F between Y and the integer lattice that translate every element of Y a bounded distance. As a corollary we get that we have such an F for any separated net that corresponds to a Penrose Tiling. The proofs rely on results of Laczkovich, and Burago and Kleiner. | |
| dc.identifier | https://arxiv.org/abs/0810.5225 | |
| dc.identifier | http://arxiv.org/abs/0810.5225 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/216239 | |
| dc.subject | Metric Geometry | |
| dc.subject | Dynamical Systems | |
| dc.title | Substitution Tilings and Separated Nets with Similarities to the Integer Lattice | |
| dc.type | text |