Uniform Distribution in Model Sets

By Robert V. Moody. Canadian mathematical bulletin, 2002

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Ergodic properties of visible lattice points (2015, methodology): “ with the Z2-action given by addition of ι(x) = ([x]p). A similar construction with translations from the group R2 in mind is given in [10]; see also [37, Ch. 5a]. The so-called torus parametrisation [28] is the Borel map ϕ: T→XV , given by ([yp]p) →M ([yp]p) + W . Clearly, ϕ intertwines the Z2-acti”
On weak model sets of extremal density (2015, background): “This name was coined by Moody [31, 32], see also [1, Rem.”
Weighted Dirac combs with pure point diffraction (2002, background): “A new direct proof and a variant without the assumption θJ (∂W ) = 0 is derived in [30].”
Dynamics on the graph of the torus parametrization (2015, methodology): “These points occur already in [43], and their importance was stressed more recently by Nicolae Strungaru [58].”
Point Sets and Dynamical Systems In the Autocorrelation Topology (2004, background): “Regular model sets are always Delone sets [5, 6 ] and have well-defined autocorrelations.”
Characterization of model sets by dynamical systems (2005, unknown): “d get Λ′′ ∈X(Λ) on the ﬁbre over (0,c) +L˜, also with p /∈Λ′′. The last statement of the Proposition is obvious. Next, let us relate the properties of W versus ∂W to the injectivity of βT. Theorem 4. [25] Let (G,H,L) be a CPS. Let M be a measurable, relatively compact set in H. Then, dens(x+f(M −h))”