Dynamical versus diffraction spectrum for structures with finite local complexity

Baake M, Lenz D, van Enter A (2015)
Ergodic Theory and Dynamical Systems 35: 2017-2043.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Baake, MichaelUniBi; Lenz, Daniel; van Enter, Aernout
Abstract / Bemerkung
It is well known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as ergodic Delone dynamical systems, both via suitable embeddings. The connection is rather well understood when the spectrum is pure point, where the two spectral notions are essentially equivalent. In general, however, the dynamical spectrum is richer. Here, we consider (uniquely) ergodic systems of finite local complexity and establish the equivalence of the dynamical spectrum with a collection of diffraction spectra of the system and certain factors. This equivalence gives access to the dynamical spectrum via these diffraction spectra. It is particularly useful as the diffraction spectra are often simpler to determine and, in many cases, only very few of them need to be calculated.
Erscheinungsjahr
2015
Zeitschriftentitel
Ergodic Theory and Dynamical Systems
Band
35
Seite(n)
2017-2043
ISSN
0143-3857
Page URI
https://pub.uni-bielefeld.de/record/2780321

Zitieren

Baake M, Lenz D, van Enter A. Dynamical versus diffraction spectrum for structures with finite local complexity. Ergodic Theory and Dynamical Systems. 2015;35:2017-2043.
Baake, M., Lenz, D., & van Enter, A. (2015). Dynamical versus diffraction spectrum for structures with finite local complexity. Ergodic Theory and Dynamical Systems, 35, 2017-2043. https://doi.org/10.1017/etds.2014.28
Baake, M., Lenz, D., and van Enter, A. (2015). Dynamical versus diffraction spectrum for structures with finite local complexity. Ergodic Theory and Dynamical Systems 35, 2017-2043.
Baake, M., Lenz, D., & van Enter, A., 2015. Dynamical versus diffraction spectrum for structures with finite local complexity. Ergodic Theory and Dynamical Systems, 35, p 2017-2043.
M. Baake, D. Lenz, and A. van Enter, “Dynamical versus diffraction spectrum for structures with finite local complexity”, Ergodic Theory and Dynamical Systems, vol. 35, 2015, pp. 2017-2043.
Baake, M., Lenz, D., van Enter, A.: Dynamical versus diffraction spectrum for structures with finite local complexity. Ergodic Theory and Dynamical Systems. 35, 2017-2043 (2015).
Baake, Michael, Lenz, Daniel, and van Enter, Aernout. “Dynamical versus diffraction spectrum for structures with finite local complexity”. Ergodic Theory and Dynamical Systems 35 (2015): 2017-2043.

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