Aperiodic Linearly Repetitive Delone Sets Are Densely Repetitive

نویسنده

  • Daniel Lenz
چکیده

We show that aperiodic linearly repetitive Delone sets are densely repetitive. This confirms a conjecture of Lagarias and Pleasants.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

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 کامل

Repetitive 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 کامل

Meyer sets, topological eigenvalues, and Cantor fiber bundles

We introduce two new characterizations of Meyer sets. A repetitive Delone set in R with finite local complexity is topologically conjugate to a Meyer set if and only if it has d linearly independent topological eigenvalues, which is if and only if it is topologically conjugate to a bundle over a d-torus with totally disconnected compact fiber and expansive canonical action. “Conjugate to” is a ...

متن کامل

Uniform Subadditive Ergodic Theorem on Aperiodic Linearly Repetitve Tilings and Applications

The paper is concerned with aperiodic linearly repetitive tilings. For such tilings we establish a weak form of self-similarity that allows us to prove general (sub)additive ergodic theorems. Finally, we provide applications to the study of lattice gas models.

متن کامل

Mathematical Quasicrystals with Toric Internal Spaces, Diffraction and Rarefaction

Aperiodic crystals viewed as Delone sets of points on the real line, having an average lattice, are studied as congruence model λ-sets (physical space is Euclidean and the equivalent of the internal space is toric) in the context of cut-and-congruence λ-schemes, a new concept. When windows are finite point sets, the fractal rates of occupancy, at infinity, of the affine lattices associated with...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete & Computational Geometry

دوره 31  شماره 

صفحات  -

تاریخ انتشار 2004