Some examples of repetitive, nonrectifiable 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 ...
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We show that aperiodic linearly repetitive Delone sets are densely repetitive. This confirms a conjecture of Lagarias and Pleasants.
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Substitution Delone set families are families of Delone sets X = (X1, . . . ,Xn) which satisfy the inflation functional equation
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This paper characterizes when a Delone setX in Rn is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the hetereogeneity of their distribution. For a Delone set X, let NX(T ) count the number of translation-inequivalent patches of radius T in X and let MX(T ) be the minimum radius such that every closed ball of radius MX(T ) contains the center ...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2016
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2016.20.1909