38 citations · 40 across the 4 of their papers we have counts for
5 papers
Directional Expansiveness for Rd-Actions and for Penrose Tilings
Hyeeun Jang, E. Arthur Robinson
We define and study two kinds of directional expansiveness, weak and strong, for an action T of \mathbb{R}^d on a compact metric space X. We show that for \mathbb{R}^2 finite local…
Directional ergodicity and weak mixing for actions of and
E. Arthur Robinson, Joseph Rosenblatt, Ayşe A. Şahin
We define notions of direction ergodicity, weak mixing, and mixing for a measure preserving action on a Lebesgue probability space , where $L\subseteq\…
Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction
Michael Baake, Natalie P. Frank, Uwe Grimm +1
One of the simplest non-Pisot substitution rules is investigated in its geometric version as a tiling with intervals of natural length as prototiles. Via a detailed renormalisation…
Parry's topological transitivity and f-expansions
E. Arthur Robinson
In his 1964 paper on f-expansions, Parry studied piecewise-continuous, piecewise-monotonic maps F of the interval [0,1), and introduced a notion of topological transitivity differe…
Generalized -expansions, substitution tilings, and local finiteness
Natalie Priebe Frank, E. Arthur Robinson
For a fairly general class of two-dimensional tiling substitutions, we prove that if the length expansion is a Pisot number, then the tilings defined by the substitution must b…