Self-affine tiling via substitution dynamical systems and Rauzy fractals

89 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions (2007, unknown): “in [33, 30, 8].”
Atomic surfaces, tilings and coincidence I. irreducible case (2006, background): “In the irreducible case, this theorem is proved in several difierent ways ([AI, SW ]).”
Topological Properties of Rauzy Fractals (2010, background): “In the irreducible case, the fact that T is compact with nonempty interior is proved in [120] and the GIFS equation is contained in [38, Theorem 2].”
Two-symbol Pisot substitutions have pure discrete spectrum (2003, background): “It was further extended in [4] and [24].”
Geometric theory of unimodular Pisot substitutions (2006, result): “A recent reference with some of the same results from the IFS point of view is [33]—see also comments in 7.”
Tilings associated with beta-numeration and substitutions. (2005, methodology): “compact non-empty sets satisfying this equation are uniquely determined [MW88]; they have non-zero measure and are the closure of their interior [ SW02 ].”