Dynamical properties of almost repetitive Delone sets
نویسندگان
چکیده
منابع مشابه
Repetitive Delone Sets and Quasicrystals
This paper studies the problem of characterizing the simplest aperiodic discrete point sets, using invariants based on topological dynamics. A Delone set of finite type is a Delone set X such that X −X is locally finite. Such sets are characterized by their patch-counting function NX(T ) of radius T being finite for all T . We formulate conjectures relating slow growth of the patch-counting fun...
متن کاملRepetitive Delone Sets and Perfect QuasicrystalsJe
This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set of nite type is a Delone set X such that X ? X is locally nite. Such sets are characterized by their patch-counting function N X (T) of radius T being nite for all T. A Delone set X of nite type is repetitive if there is a function ...
متن کاملAperiodic Linearly Repetitive Delone Sets Are Densely Repetitive
We show that aperiodic linearly repetitive Delone sets are densely repetitive. This confirms a conjecture of Lagarias and Pleasants.
متن کاملErrata to “spectrum of Dynamical Systems Arising from Delone Sets”
1. Lenz and Stollman [3] pointed out that the “metric” ρ defined on page 266 of [4] does not satisfy the triangle inequality. There we used for two Delone sets Λ1 and Λ2, denoting by Br the ball of radius r centered at the origin: ρ(Λ1,Λ2) = min{2−1/2, ρ̃(Λ1,Λ2)}, where ρ̃(Λ1,Λ2) = inf{ > 0 : dH [Λ1 ∩B1/ , Λ2 ∩B1/ ] ≤ } . Here dH is the Hausdorff distance. There are several ways to fix this, desc...
متن کاملSpectrum of dynamical systems arising from Delone sets
We investigate spectral properties of the translation action on the orbit closure of a Delone set. In particular, suucient conditions for pure discrete spectrum are given, based on the notion of almost periodicity. Connections with diiraction spectrum are discussed.
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2013
ISSN: 1078-0947
DOI: 10.3934/dcds.2014.34.531