146 citations
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math.DS2020★ 4 cited
Rotation numbers and rotation classes on one-dimensional tiling spaces
José Aliste-Prieto, Betseygail Rand, Lorenzo Sadun
We extend rotation theory of circle maps to tiling spaces. Specifically, we consider a 1-dimensional tiling space with finite local complexity and study self-maps that are…
math.DS2009
An Approximation Theorem for Maps Between Tiling Spaces
Betseygail Rand, Lorenzo Sadun
We show that every continuous map from one translationally finite tiling space to another can be approximated by a local map. If two local maps are homotopic, then the homotopy can…