Repetitive Delone sets and quasicrystals
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 کاملGeometric Models for Quasicrystals I. Delone Sets of Finite Type
This paper studies three classes of discrete sets X in R n which have a weak translational order imposed by increasingly strong restrictions on their sets of interpoint vectors X ? X. A nitely generated Delone set is one such that the abelian group X ? X] generated by X ? X is nitely generated, so that X ? X] is a lattice or a quasilattice. For such sets the abelian group X] is nitely generated...
متن کاملSubstitution Delone Sets
Substitution Delone set families are families of Delone sets X = (X1, . . . ,Xn) which satisfy the inflation functional equation
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2003
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385702001566