Optimal embedding of Meyer sets into model sets
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- by Jean-Baptiste Aujogue PDF
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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
- J-B. Aujogue, On embedding of repetitive meyer multiple sets into model multiple sets, to appear in Ergodic Theory and Dynamical Systems (2014).
- 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, DOI 10.1307/mmj/1387226166
- Karl H. Hofmann and Sidney A. Morris, Open mapping theorem for topological groups, Topology Proc. 31 (2007), no. 2, 533–551. MR 2476628
- Johannes Kellendonk, Noncommutative geometry of tilings and gap labelling, Rev. Math. Phys. 7 (1995), no. 7, 1133–1180. MR 1359991, DOI 10.1142/S0129055X95000426
- 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, DOI 10.1017/S0143385702001566
- 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, DOI 10.1007/s00023-005-0244-6
- 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, DOI 10.1007/s00454-008-9054-1
- 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, DOI 10.3934/dcds.2012.32.935
- 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
- 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.
- 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
- Nicolae Strungaru, On the Bragg diffraction spectra of a Meyer set, Canad. J. Math. 65 (2013), no. 3, 675–701. MR 3043047, DOI 10.4153/CJM-2012-032-1
Additional Information
- Jean-Baptiste Aujogue
- Affiliation: Departamento de Matemáticas, Facultad de Ciencia, Universidad de Santiago de Chile, Santiago, Chile
- Email: jean.baptiste@usach.cl
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1277-1288
- MSC (2010): Primary 37B50, 52C23
- DOI: https://doi.org/10.1090/proc/12790
- MathSciNet review: 3447678