Higher dimensional extensions of substitutions and their dual maps
By Yukihiro Sano, Pierre Arnoux, Shunji Ito. 2001
73 citations recorded by the source corpus.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4980574a0135fbcc47210f35e790b93dbe6251ad
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
- Anne Siegel
- Val'erie Berth'e
- Jörg M. Thuswaldner
- Marcy Barge
- Jaroslaw Kwapisz
- Shunji Ito
- Shigeki Akiyama
- Víctor F. Sirvent
In Geometry and Topology
In Mathematical Physics
- Anne Siegel
- Val'erie Berth'e
- Jörg M. Thuswaldner
- Marcy Barge
- Jaroslaw Kwapisz
- Shunji Ito
- Shigeki Akiyama
- Yang Wang
Citations in the corpus
- Geometric theory of unimodular Pisot substitutions (2006, background): “) As it turns out, F∗ φ comes with a natural inflation-substitution dynamics closely related to the generalized dual substitution Θ devised by Arnoux and Ito [2] (see also [3] and 8.”
- Pisot substitutions and Rauzy fractals (2001, background): “Another problem is given by the case of unimodular non-Pisot substitutions; we give some elements to study this problem in [AIS00], generalizing the construction of linear extensions of substitutions and their dual maps.”
- Topological Properties of Rauzy Fractals (2010, methodology): “This idea is formalized by homology-like objects in [25, 114], and produces Rauzy fractals.”
- Tilings associated with beta-numeration and substitutions. (2005, methodology): “The second approach via Iterated Function Systems and generalized substitutions has been developed following ideas from [Thu89, IK91], and [AI01, SAI01 ]: central tiles are described as attractors of some graph-directed IFS, as developed in [HZ98, Sir00a, Sir00b, SW02].”