Pisot substitutions and Rauzy fractals
By Pierre Arnoux, Shunji Ito. 2001
278 citations recorded by the source corpus.
Subfields: Artificial Intelligence, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e6848b2c7ed15e471df925029ad7090667a029ef
How researchers see this paper
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In Artificial Intelligence
- Shigeki Akiyama
- Val'erie Berth'e
- Anne Siegel
- Vincent Delecroix
- Víctor F. Sirvent
- Jörg M. Thuswaldner
- Yang Wang
In Computational Theory and Mathematics
- Anne Siegel
- Val'erie Berth'e
- Jörg M. Thuswaldner
- Marcy Barge
- Vincent Delecroix
- Shigeki Akiyama
- Jaroslaw Kwapisz
- J.-Y. Lee
In Mathematical Physics
- Anne Siegel
- Val'erie Berth'e
- Jörg M. Thuswaldner
- Marcy Barge
- Shigeki Akiyama
- Vincent Delecroix
- Jaroslaw Kwapisz
- Boris Solomyak
Citations in the corpus
- Geometric theory of unimodular Pisot substitutions (2006, background): “Dekking’s condition was generalized to the nonconstant length case by Arnoux and Ito [2] and independently by Hollander and Solomyak [12].”
- Self-affine tiling via substitution dynamical systems and Rauzy fractals (2002, methodology): “The geometric and dynamical properties of Rauzy fractals have been studied in a number of papers, among others see [ 1 , 9, 23, 27, 28, 30].”
- Topological Properties of Rauzy Fractals (2010, methodology): “The proof for the disjointness is given in [25] for the irreducible case and generalized to the reducible case in [38, 61].”
- Two-symbol Pisot substitutions have pure discrete spectrum (2003, background): “However, being a domain exchange does not automatically imply that the dynamical system is pure discrete and additional conditions were needed to make such a claim [1, 21].”
- Tilings associated with beta-numeration and substitutions. (2005, methodology): “A formal and precise definition appears in [AI01]: a substitution is said to satisfy the strong coincidence condition if for any pair of letters (i, j), there exist two integers k, n such that σ(i) and σ(i) have the same k-th letter, and the prefixes of length k− 1 of σ(i) and σ(j) have the same ima”
- On the Pisot Substitution Conjecture (2015, background): “As a consequence, further combinatorial formulations of the pure discrete spectrum property can be stated in effective terms (see [14, 39] for more detail).”
- Beyond substitutive dynamical systems: S-adic expansions (2013, background): “In particular cases, namely substitutive Arnoux‐Rauzy words, the Pisot conjecture is known to hold [13, 34].”