Pure point diffraction implies zero entropy for Delone sets with uniform cluster frequencies

被引：27

作者：

Baake, Michael

Lenz, Daniel

Richard, Christoph

机构：

[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

[2] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2007年 / 82卷 / 01期

关键词：

Delone sets; entropy; model sets; substitutions;

D O I：

10.1007/s11005-007-0186-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Delone sets of finite local complexity in Euclidean space are investigated. We show that such a set has patch counting and topological entropy zero if it has uniform cluster frequencies and is pure point diffractive. We also note that the patch counting entropy vanishes whenever the repetitivity function satisfies a certain growth restriction.

引用

页码：61 / 77

页数：17

共 9 条

[1] Pure Point Diffraction Implies Zero Entropy for Delone Sets with Uniform Cluster Frequencies
Michael Baake
Daniel Lenz
Christoph Richard
[J]. Letters in Mathematical Physics, 2007, 82 : 61 - 77
[2] Deformation of Delone Dynamical Systems and Pure Point Diffraction
Michael Baake
Daniel Lenz
[J]. Journal of Fourier Analysis and Applications, 2005, 11 : 125 - 150
[3] Deformation of delone dynamieal systems and pure point diffraction
Baake, M
Lenz, D
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2005, 11 (02) : 125 - 150
[4] Substitution Delone sets with pure point spectrum are inter-model sets
Lee, Jeong-Yup
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2007, 57 (11) : 2263 - 2285
[5] Pure point diffractive substitution Delone sets have the Meyer property
Lee, Jeong-Yup
Solomyak, Boris
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2008, 39 (1-3) : 319 - 338
[6] Pure Point Diffractive Substitution Delone Sets Have the Meyer Property
Jeong-Yup Lee
Boris Solomyak
[J]. Discrete & Computational Geometry, 2008, 39 : 319 - 338
[7] Pure point diffraction and entropy beyond the Euclidean space
Hauser, T.
[J]. INDAGATIONES MATHEMATICAE-NEW SERIES, 2024, 35 (05): : 1057 - 1074
[8] Zero sets and uniqueness sets with one cluster point for the Dirichlet space
Mashreghi, Javad
Shabankhah, Mahmood
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 357 (02) : 498 - 503
[9] A short guide to pure point diffraction in cut-and-project sets
Richard, Christoph
Strungaru, Nicolae
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2017, 50 (15)

← 1 →