Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra

MICHAEL BAAKE; DANIEL LENZ

doi:10.1017/S0143385704000318

Abstract

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Certain topological dynamical systems that arise from actions of $\sigma$-compact locally compact Abelian groups on compact spaces of translation bounded measures are considered. Such a measure dynamical system is shown to have a pure point dynamical spectrum if and only if its diffraction spectrum is pure point.

Crossref Citations

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Sadun, L. 2006. Tilings, tiling spaces and topology. Philosophical Magazine, Vol. 86, Issue. 6-8, p. 875.

Lee, J.-Y. 2006. Quasicrystals and model sets on substitution point sets. Philosophical Magazine, Vol. 86, Issue. 6-8, p. 915.

Lee, Jeong-Yup 2007. Substitution Delone sets with pure point spectrum are inter-model sets. Journal of Geometry and Physics, Vol. 57, Issue. 11, p. 2263.

Lenz, Daniel and Richard, Christoph 2007. Pure point diffraction and cut and project schemes for measures: the smooth case. Mathematische Zeitschrift, Vol. 256, Issue. 2, p. 347.

Baake, M. Frettlöh, D. and Grimm, U. 2007. Pinwheel patterns and powder diffraction. Philosophical Magazine, Vol. 87, Issue. 18-21, p. 2831.

Baake, Michael Frettlöh, Dirk and Grimm, Uwe 2007. A radial analogue of Poisson’s summation formula with applications to powder diffraction and pinwheel patterns. Journal of Geometry and Physics, Vol. 57, Issue. 5, p. 1331.

Baake, Michael Lenz, Daniel and Richard, Christoph 2007. Pure Point Diffraction Implies Zero Entropy for Delone Sets with Uniform Cluster Frequencies. Letters in Mathematical Physics, Vol. 82, Issue. 1, p. 61.

Deng, Xinghua and Moody, Robert V. 2008. Dworkin’s argument revisited: Point processes, dynamics, diffraction, and correlations. Journal of Geometry and Physics, Vol. 58, Issue. 4, p. 506.

Lenz, D. 2008. Aperiodic order and pure point diffraction. Philosophical Magazine, Vol. 88, Issue. 13-15, p. 2059.

Akiyama, Shigeki and Kwon, Do Yong 2008. Constructions of Pisot and Salem numbers with flat palindromes. Monatshefte für Mathematik, Vol. 155, Issue. 3-4, p. 265.

Frank, Natalie Priebe 2008. A primer of substitution tilings of the Euclidean plane. Expositiones Mathematicae, Vol. 26, Issue. 4, p. 295.

Baake, Michael and Zint, Natali 2008. Absence of Singular Continuous Diffraction for Discrete Multi-Component Particle Models. Journal of Statistical Physics, Vol. 130, Issue. 4, p. 727.

Frettlöh, Dirk 2008. Substitution tilings with statistical circular symmetry. European Journal of Combinatorics, Vol. 29, Issue. 8, p. 1881.

Lee, Jeong-Yup and Solomyak, Boris 2008. Pure Point Diffractive Substitution Delone Sets Have the Meyer Property. Discrete & Computational Geometry, Vol. 39, Issue. 1-3, p. 319.

Frettlöh, D. 2008. About substitution tilings with statistical circular symmetry. Philosophical Magazine, Vol. 88, Issue. 13-15, p. 2033.

Moody, Robert V. 2008. Recent developments in the mathematics of diffraction. Zeitschrift für Kristallographie, Vol. 223, Issue. 11-12, p. 795.

Lenz, Daniel and Moody, Robert V. 2009. Extinctions and Correlations for Uniformly Discrete Point Processes with Pure Point Dynamical Spectra. Communications in Mathematical Physics, Vol. 289, Issue. 3, p. 907.

Lenz, Daniel 2009. Continuity of Eigenfunctions of Uniquely Ergodic Dynamical Systems and Intensity of Bragg Peaks. Communications in Mathematical Physics, Vol. 287, Issue. 1, p. 225.

Lenz, Daniel and Strungaru, Nicolae 2009. Pure point spectrum for measure dynamical systems on locally compact Abelian groups. Journal de Mathématiques Pures et Appliquées, Vol. 92, Issue. 4, p. 323.

Baake, Michael and Ward, Tom 2010. Planar Dynamical Systems with Pure Lebesgue Diffraction Spectrum. Journal of Statistical Physics, Vol. 140, Issue. 1, p. 90.

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Dynamical systems on translation bounded measures: pure point dynamical and diffraction spectra

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