Symbolic and geometric representations of unimodular Pisot substitutions
| dc.contributor.author | Wieler, Susana | |
| dc.contributor.supervisor | Putnam, Ian | |
| dc.date.accessioned | 2007-07-11T18:23:24Z | |
| dc.date.available | 2007-07-11T18:23:24Z | |
| dc.date.copyright | 2007 | en_US |
| dc.date.issued | 2007-07-11T18:23:24Z | |
| dc.degree.department | Dept. of Mathematics and Statistics | en_US |
| dc.degree.level | Master of Science M.Sc. | en_US |
| dc.description.abstract | We review the construction of three Smale spaces associated to a unimodular Pisot substitution on d letters: a subshift of finite type (SFT), a substitution tiling space, and a hyperbolic toral automorphism on the Euclidean d-torus. By considering an SFT whose elements are biinfinite, rather than infinite, paths in the graph associated to the substitution, we modify a well-known map to obtain a factor map between our SFT and the hyperbolic toral automorphism on the d-torus given by the incidence matrix of the substitution. We prove that if the tiling substitution forces its border, then this factor map is the composition of an s-resolving factor map from the SFT to a one-dimensional substitution tiling space and a u-resolving factor map from the tiling space to the d-torus. | en_US |
| dc.identifier.uri | http://hdl.handle.net/1828/131 | |
| dc.language | English | eng |
| dc.language.iso | en | en_US |
| dc.rights | Available to the World Wide Web | en_US |
| dc.subject | substitutions | en_US |
| dc.subject | dynamical systems | en_US |
| dc.subject | tilings | en_US |
| dc.subject | Smale spaces | en_US |
| dc.subject | Pisot | en_US |
| dc.subject | hyperbolic toral automorphism | en_US |
| dc.subject | subshift of finite type | en_US |
| dc.subject.lcsh | UVic Subject Index::Sciences and Engineering::Mathematics::Pure mathematics | en_US |
| dc.title | Symbolic and geometric representations of unimodular Pisot substitutions | en_US |
| dc.type | Thesis | en_US |