PL EN


Preferences help
enabled [disable] Abstract
Number of results
2014 | 126 | 2 | 431-434
Article title

Scaling of the Thue-Morse Diffraction Measure

Content
Title variants
Languages of publication
EN
Abstracts
EN
We revisit the well-known and much studied Riesz product representation of the Thue-Morse diffraction measure, which is also the maximal spectral measure for the corresponding dynamical spectrum in the complement of the pure point part. The known scaling relations are summarised, and some new findings are explained.
Keywords
EN
Year
Volume
126
Issue
2
Pages
431-434
Physical description
Dates
published
2014-08
References
  • [1] J.-P. Allouche, J. Shallit, Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, Cambridge 2003
  • [2] M. Baake, U. Grimm, Aperiodic Order, Vol. 1: A Mathematical Invitation, Cambridge University Press, Cambridge 2013
  • [3] M. Keane, Z. Wahrscheinlichkeitsth. verw. Geb. 10, 335 (1968), doi: 10.1007/BF00531855
  • [4] M. Queffélec, Substitution Dynamical Systems - Spectral Analysis, LNM 1294, 2nd ed., Springer, Berlin 2010
  • [5] A.C.D. van Enter, J. Miękisz, J. Stat. Phys. 66, 1147 (1992), doi: 10.1007/BF01055722
  • [6] M. Baake, U. Grimm, J. Phys. A: Math. Theor. 41, 422001 (2008), doi: 10.1088/1751-8113/41/42/422001
  • [7] A. Zygmund, Trigonometric Series, 3rd ed., Cambridge University Press, Cambridge 2002
  • [8] N.P. Frank, Topol. Appl. 152, 44 (2005), doi: 10.1016/j.topol.2004.08.014
  • [9] N. Wiener, J. Math. Massachusetts 6, 145 (1927)
  • [10] K. Mahler, J. Math. Massachusetts 6, 158 (1927)
  • [11] S. Kakutani, in: Proc. 6th Berkeley Symp. on Math. Statistics and Probability, Eds. L.M. LeCam, J. Neyman, E.L. Scott, Univ. of California Press, Berkeley 1972, p. 319
  • [12] R.L. Withers, Z. Krist. 220, 1027 (2005), doi: 10.1524/zkri.2005.220.12.1027
  • [13] Z. Cheng, R. Savit, R. Merlin, Phys. Rev. B 37, 4375 (1988), doi: 10.1364/JOSAB.29.002130
  • [14] C. Godréche, J.M. Luck, J. Phys. A, Math. Gen. 23, 3769 (1990), doi: 10.1088/0305-4470/23/16/024
  • [15] M.A. Zaks, J. Phys. A, Math. Gen. 35, 5833 (2002), doi: 10.1088/0305-4470/35/28/304
  • [16] M.A. Zaks, A.S. Pikovsky, J. Kurths, J. Stat. Phys. 88, 1387 (1997), doi: 10.1007/BF02732440
  • [17] M.A. Zaks, A.S. Pikovsky, J. Kurths, J. Phys. A, Math. Gen. 32, 1523 (1999), doi: 10.1088/0305-4470/32/8/018
  • [18] L. Kuipers, H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York 1974; reprint Dover, New York 2006
  • [19] M. Kac, Ann. Math. 47, 33 (1946), doi: 10.2307/1969033
  • [20] G.H. Hardy, J.E. Littlewood, Acta Math. 37, 155 (1914), doi: 10.1007/BF02401833
  • [21] N.J.A.S. Sloane, The On-Line Encyclopedia of Integer Sequences, http://oeis.org
  • [22] M. Baake, F. Gähler, U. Grimm, J. Math. Phys. 53, 032701 (2012), doi: 10.1063/1.3688337
  • [23] J. Wolny, A. Wnęk, J.-L. Verger-Gaugry, J. Comput. Phys. 163, 313 (2000), doi: 10.1006/jcph.2000.6563
  • [24] M. Baake, U. Grimm, Erg. Th. Dynam. Syst., arXiv:1205.1384
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv126n201kz
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.