9 citations · 20 across the 12 of their papers we have counts for
5 papers · 1 filter
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…
On the simplicity of homeomorphism groups of a tilable lamination
José Aliste-Prieto, Samuel Petite
We show that the identity component of the group of homeomorphisms that preserve all leaves of a R^d-tilable lamination is simple. Moreover, in the one dimensional case, we show th…
Almost periodic structures and the semiconjugacy problem
José Aliste-Prieto, Tobias Jäger
The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. F…
Linearly repetitive Delone sets are rectifiable
J. Aliste-Prieto, D. Coronel, J. -M. Gambaudo
In this paper we prove that, for any integer , every linearly repetitive Delone set in the Euclidean -space $\RR^d$ is equivalent, up to a bi-Lipschitz homeomorphism, to th…
Tower systems for Linearly repetitive Delone sets
José Aliste-Prieto, Daniel Coronel
In this paper we study linearly repetitive Delone sets and prove, following the work of Bellissard, Benedetti and Gambaudo, that the hull of a linearly repetitive Delone set admits…