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2014 | 126 | 2 | 539-542
Article title

On a Family of Random Noble Means Substitutions

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EN
Abstracts
EN
In 1989, Godrèche and Luck introduced the concept of local mixtures of primitive substitution rules along the example of the well-known Fibonacci substitution and foreshadowed heuristic results on the topological entropy and the spectral type of the diffraction measure of associated point sets. In this contribution, we present a generalisation of this concept by regarding the so-called "noble means families", each consisting of finitely many primitive substitution rules that individually all define the same two-sided discrete dynamical hull. We report about results in the randomised case on topological entropy, ergodicity of the two-sided discrete hull, and the spectral type of the diffraction measure of related point sets.
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EN
Publisher

Year
Volume
126
Issue
2
Pages
539-542
Physical description
Dates
published
2014-08
Contributors
author
  • Fakultät für Mathematik, Universität Bielefeld, Universitätsstraÿe 25, D-33615 Bielefeld, Germany
References
  • [1] C. Godrèche, J.M. Luck, J. Stat. Phys. 55, 1 (1989), doi: 10.1007/BF01042590
  • [2] M. Baake, U. Grimm, Aperiodic Order, Vol. 1, A Mathematical Invitation, Cambridge University Press, Cambridge 2013
  • [3] J. Nilsson, Monatsh. Math. 166, 1 (2012), doi: 10.1007/s00605-012-0401-1
  • [4] M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, 2nd ed., LNM 1294, Springer, Berlin 2010, doi: 10.1007/978-3-642-11212-6
  • [5] M. Moll, Ph.D. Thesis, University of Bielefeld, 2013. http://pub.uni-bielefeld.de/publication/2637807
  • [6] M. Baake, M. Moll, in: Aperiodic Crystals, Eds. S. Schmid, R.L. Withers, R. Lifshitz, Springer, Dordrecht 2013, p. 19, doi: 10.1007/978-94-007-6431-6
  • [7] N. Etemadi, Z. Wahrscheinlichkeitsth. verw. Geb. 55, 119 (1981), doi: 10.1007/BF01013465
  • [8] R.V. Moody, in: The Mathematics of Long-Range Aperiodic Order, Ed. R.V. Moody, NATO ASI Series C 489, Kluwer, Dordrecht 1997, p. 403
  • [9] N. Strungaru, Can. J. Math. 65, 675 (2013), doi: 10.4153/CJM-2012-032-1
  • [10] M. Baake, D. Lenz, C. Richard, Lett. Math. Phys. 82, 61 (2007), doi: 10.1007/s11005-007-0186-7
  • [11] I.P. Cornfeld, S.V. Fomin, Y.G. Sinai, Ergodic Theory, Springer, New York 1982, doi: 10.1007/978-1-4615-6927-5
  • [12] M. Einsiedler, T. Ward, Ergodic Theory: With a View towards Number Theory, Springer, London (2011), doi: 10.1007/978-0-85729-021-2
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv126n229kz
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