Delone Sets with Finite Local Complexity: Linear Repetitivity Versus Positivity of Weights

被引：8

作者：

Besbes, Adnene ^{[1
]}

Boshernitzan, Michael ^{[2
]}

Lenz, Daniel ^{[3
]}

机构：

[1] Univ Tunis El Manar, IPEI Bizerte, Zarzouna, Bizerte, Tunisia

[2] Rice Univ, Houston, TX 77251 USA

[3] Univ Jena, Math Inst, D-07743 Jena, Germany

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2013年 / 49卷 / 02期

基金：

美国国家科学基金会;

关键词：

Delone sets; Linear repetitivity; Subadditive ergodic theorem; UNIFORM ERGODIC-THEOREMS; TILINGS;

D O I：

10.1007/s00454-012-9455-z

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider Delone sets with finite local complexity. We characterize the validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this context, we show that linear repetitivity is equivalent to positivity of weights combined with a certain balancedness of the shape of return patterns.

引用

页码：335 / 347

页数：13

共 8 条

[1] Delone Sets with Finite Local Complexity: Linear Repetitivity Versus Positivity of Weights
Adnene Besbes
Michael Boshernitzan
Daniel Lenz
[J]. Discrete & Computational Geometry, 2013, 49 : 335 - 347
[2] ON SUBSTITUTION TILINGS AND DELONE SETS WITHOUT FINITE LOCAL COMPLEXITY
Lee, Jeong-Yup
Solomyak, Boris
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (06) : 3149 - 3177
[3] Local complexity of Delone sets and crystallinity
Lagarias, JC
Pleasants, PAB
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2002, 45 (04): : 634 - 652
[4] LATTICE BOUNDED DISTANCE EQUIVALENCE FOR 1D DELONE SETS WITH FINITE LOCAL COMPLEXITY
Ambroz, Petr
Masakova, Zuzana
Pelantova, Edita
[J]. JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, 2021, 59 : 1 - 29
[5] ESTIMATION OF COMPLEXITY OF LOCAL ALGORITHMS FOR CERTAIN EXTREMUM PROBLEMS ON FINITE SETS
ZHURAVLEV, YI
[J]. DOKLADY AKADEMII NAUK SSSR, 1964, 158 (05): : 1018 - +
[6] DELONE MEASURES OF FINITE LOCAL COMPLEXITY AND APPLICATIONS TO SPECTRAL THEORY OF ONE-DIMENSIONAL CONTINUUM MODELS OF QUASICRYSTALS
Klassert, Steffen
Lenz, Daniel
Stollmann, Peter
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 29 (04) : 1553 - 1571
[7] Dynamical versus diffraction spectrum for structures with finite local complexity
Baake, Michael
Lenz, Daniel
van Enter, Aernout
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2015, 35 : 2017 - 2043
[8] Octagonal and hexadecagonal cut algorithms for finding the convex hull of finite sets with linear time complexity
Hoang, Nam-Dung
Linh, Nguyen Kieu
Phu, Hoang Xuan
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2024, 481

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