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Topological properties of Rauzy fractals

Author: Anne Siegel; Jörg M Thuswaldner
Publisher: Paris : Sociéte Mathématique de France, 2009.
Series: Mémoire (Société mathématique de France), nouv. sér., no 118.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
Rauzy fractals play a major role in many branches of mathematics including number theory, dynamical systems, combinatorics and a theory of quasicrystals. In many problems the topological structure of Rauzy fractals is of crucial importance. This monograph continues a systematic study of topological properties of Rauzy fractals. After a thorough survey on basic results on these fractals, we aim at collective known  Read more...
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Document Type: Book
All Authors / Contributors: Anne Siegel; Jörg M Thuswaldner
ISBN: 9782856292907 2856292909
OCLC Number: 693373358
Description: 140 pages : illustrations ; 24 cm.
Contents: Introduction --
Substitutions, central tiles and beta-numeration --
Multiple tilings induced by the central tile and its subtiles --
Statement of the main results : topological properties of central tiles --
Graphs that contain topological information on the central tile --
Exact statements and proofs of the main results --
Technical proofs and definitions --
Perspectives.
Series Title: Mémoire (Société mathématique de France), nouv. sér., no 118.
Responsibility: Anne Siegel, Jörg M. Thuswaldner.

Abstract:

Rauzy fractals play a major role in many branches of mathematics including number theory, dynamical systems, combinatorics and a theory of quasicrystals. In many problems the topological structure of Rauzy fractals is of crucial importance. This monograph continues a systematic study of topological properties of Rauzy fractals. After a thorough survey on basic results on these fractals, we aim at collective known results on the topology of Rauzy fractals and prove a variety of new ones. We investigate tiling properties, connectivity, homeomorphy to a closed disk as well as the fundamental group of Rauzy fractals. Our main tools are results from plane topology and certain classes of graphs that are defined in terms of tiling properties of Rauzy fractals. We illustrate all our results with many examples.

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