Linearly repetitive Delone sets are rectifiable
نویسندگان
چکیده
منابع مشابه
Aperiodic 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 کاملRepetitive 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 کاملSubstitution Delone Sets
Substitution Delone set families are families of Delone sets X = (X1, . . . ,Xn) which satisfy the inflation functional equation
متن کاملInformation Theory on Rectifiable Sets
Entropy and—maybe even more so—mutual information are invaluable tools for analyzing properties of probability distributions, especially in coding theory. While there are general definitions for both concepts available for arbitrary probability distributions, these tend to be hard to work with and the literature (e.g., [CT06]) focuses on either discrete, or continuous random variables. In this ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
سال: 2013
ISSN: 0294-1449
DOI: 10.1016/j.anihpc.2012.07.006