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