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 
admits a smallest model multiple set containing it colorwise.
- [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
- [4] Johannes Kellendonk, Noncommutative geometry of tilings and gap labelling, Rev. Math. Phys. 7 (1995), no. 7, 1133–1180. MR 1359991, 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, 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, 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, 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
- [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
- [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
- [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
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
