Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Optimal embedding of Meyer sets into model sets


Author: Jean-Baptiste Aujogue
Journal: Proc. Amer. Math. Soc. 144 (2016), 1277-1288
MSC (2010): Primary 37B50, 52C23
DOI: https://doi.org/10.1090/proc/12790
Published electronically: August 5, 2015
MathSciNet review: 3447678
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give a constructive proof that a repetitive Meyer multiple set of $ \mathbb{R}^d$ admits a smallest model multiple set containing it colorwise.


References [Enhancements On Off] (What's this?)

  • [1] J-B. Aujogue, On embedding of repetitive meyer multiple sets into model multiple sets, to appear in Ergodic Theory and Dynamical Systems (2014).
  • [2] Marcy Barge and Johannes Kellendonk, Proximality and pure point spectrum for tiling dynamical systems, Michigan Math. J. 62 (2013), no. 4, 793-822. MR 3160543, https://doi.org/10.1307/mmj/1387226166
  • [3] Karl H. Hofmann and Sidney A. Morris, Open mapping theorem for topological groups, Topology Proc. 31 (2007), no. 2, 533-551. MR 2476628 (2010a:22027)
  • [4] Johannes Kellendonk, Noncommutative geometry of tilings and gap labelling, Rev. Math. Phys. 7 (1995), no. 7, 1133-1180. MR 1359991 (96m:46132), https://doi.org/10.1142/S0129055X95000426
  • [5] Jeffrey C. Lagarias and Peter A. B. Pleasants, Repetitive Delone sets and quasicrystals, Ergodic Theory Dynam. Systems 23 (2003), no. 3, 831-867. MR 1992666 (2005a:52018), https://doi.org/10.1017/S0143385702001566
  • [6] Jeong-Yup Lee and Robert V. Moody, A characterization of model multi-colour sets, Ann. Henri Poincaré 7 (2006), no. 1, 125-143. MR 2205466 (2007f:52046), https://doi.org/10.1007/s00023-005-0244-6
  • [7] Jeong-Yup Lee and Boris Solomyak, Pure point diffractive substitution Delone sets have the Meyer property, Discrete Comput. Geom. 39 (2008), no. 1-3, 319-338. MR 2383764 (2008m:52045), https://doi.org/10.1007/s00454-008-9054-1
  • [8] Jeong-Yup Lee and Boris Solomyak, Pisot family self-affine tilings, discrete spectrum, and the Meyer property, Discrete Contin. Dyn. Syst. 32 (2012), no. 3, 935-959. MR 2851885 (2012h:37040)
  • [9] Robert V. Moody, Meyer sets and their duals, The mathematics of long-range aperiodic order (Waterloo, ON, 1995), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 489, Kluwer Acad. Publ., Dordrecht, 1997, pp. 403-441. MR 1460032 (98e:52029)
  • [10] R.V. Moody, Model sets: A survey, From Quasicrystals to More Complex Systems, Centre de Physique des Houches, vol. 13, Springer, Berlin, Heidelberg, 2000, pp. 145-166.
  • [11] Martin Schlottmann, Generalized model sets and dynamical systems, Directions in mathematical quasicrystals, CRM Monogr. Ser., vol. 13, Amer. Math. Soc., Providence, RI, 2000, pp. 143-159. MR 1798991 (2001k:52035)
  • [12] Nicolae Strungaru, On the Bragg diffraction spectra of a Meyer set, Canad. J. Math. 65 (2013), no. 3, 675-701. MR 3043047, https://doi.org/10.4153/CJM-2012-032-1

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37B50, 52C23

Retrieve articles in all journals with MSC (2010): 37B50, 52C23


Additional Information

Jean-Baptiste Aujogue
Affiliation: Departamento de Matemáticas, Facultad de Ciencia, Universidad de Santiago de Chile, Santiago, Chile
Email: jean.baptiste@usach.cl

DOI: https://doi.org/10.1090/proc/12790
Keywords: Meyer set, model set, proximality
Received by editor(s): November 28, 2014
Received by editor(s) in revised form: March 11, 2015, and March 24, 2015
Published electronically: August 5, 2015
Additional Notes: The author thanks the Universidad de Santiago de Chile and Proyecto POSTDOC$_$DICYT Código 001316POSTDOC, Vicerrectoria de Investigación, Desarrollo e Innovación.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society