Topological properties of tiles

Benoit Loridant

Topological properties of tiles

Titel in Übersetzung: Topologische Eigenschaften von Tiles

Benoit Loridant

Lehrstuhl für Mathematik, Statistik und Geometrie (380)

Publikation: Thesis / Studienabschlussarbeiten und Habilitationsschriften › Dissertation

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Abstract

Die Topologie von fraktalen Pflastern, die Pflasterungen der Ebene zugrunde liegen, wird untersucht. Dabei werden Kriteria für die Homöomorphie der Pflaster zu einer Kreisscheibe angegeben. Von Wichtigkeit erweisen sich die Nachbarschaftsrelationen innerhalb der Pflasterung. Eine Klasse von Pflastern, die Beziehungen zu kanonischen Ziffernsystemen haben, wird betrachtet. Unter anderem kann eine Komponente des Inneren eines solchen Pflasters mit Hilfe eines endlichen Graphen beschrieben werden.

Titel in Übersetzung	Topologische Eigenschaften von Tiles
Originalsprache	Englisch
Qualifikation	Dr.mont.
Betreuer/-in / Berater/-in	Thuswaldner, Jörg, Beurteiler A (intern) Drmota, Michael, Beurteiler B (extern), Externe Person
Publikationsstatus	Veröffentlicht - 2007

Bibliographische Notiz

gesperrt bis null

Schlagwörter

selbst-affine Pflaster
kristallographische Pflasterungen
kanonische Ziffernsysteme

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abstract = "The topology of fractal tiles giving rise to a tessellation of the plane is investigated. This work leads to several criteria for a tile to be homeorphic to a closed disk. The criteria are all established by considering the neighbor configurations of the tiles in the tiling. A special class of tiles associated to canonical number systems is studied. The inner component of such a tile is described with the help of a finite graph.",

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N2 - The topology of fractal tiles giving rise to a tessellation of the plane is investigated. This work leads to several criteria for a tile to be homeorphic to a closed disk. The criteria are all established by considering the neighbor configurations of the tiles in the tiling. A special class of tiles associated to canonical number systems is studied. The inner component of such a tile is described with the help of a finite graph.

AB - The topology of fractal tiles giving rise to a tessellation of the plane is investigated. This work leads to several criteria for a tile to be homeorphic to a closed disk. The criteria are all established by considering the neighbor configurations of the tiles in the tiling. A special class of tiles associated to canonical number systems is studied. The inner component of such a tile is described with the help of a finite graph.

KW - selbst-affine Pflaster

KW - kristallographische Pflasterungen

KW - kanonische Ziffernsysteme

KW - self-affine tiles

KW - crystallographic tilings

KW - canonical number systems

M3 - Doctoral Thesis

ER -