35 citations · 71 across the 14 of their papers we have counts for
18 papers
Complete regularity of Ellis semigroups of -actions
Marcy Barge, Johannes Kellendonk
It is shown that the Ellis semigroup of a -action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward…
The Pisot Conjecture for -substitutions
Marcy Barge
We prove the Pisot Conjecture for beta-substitutions: If beta is a Pisot number, the tiling dynamical system associated with the beta-substitution has pure discrete spectrum. As co…
Equicontinuous factors, proximality and Ellis semigroup for Delone sets
Jean-baptiste Aujogue, Marcy Barge, Johannes Kellendonk +1
We discuss the application of various concepts from the theory of topological dynamical systems to Delone sets and tilings. We consider in particular, the maximal equicontinuous fa…
Pure discrete spectrum for a class of one-dimensional substitution tiling systems
Marcy Barge
We prove that if a primitive and non-periodic substitution is injective on initial letters, constant on final letters, and has Pisot inflation, then the R-action on the correspondi…
Factors of Pisot tiling spaces and the coincidence rank conjecture
Marcy Barge
We consider the structure of Pisot substitution tiling spaces, in particular, the structure of those spaces for which the translation action does not have pure discrete spectrum. S…
Maximal equicontinuous factors and cohomology for tiling spaces
Marcy Barge, Johannes Kellendonk, Scott Schmieding
We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that this map is injective in degree one and has torsion fre…