6 citations · 13 across the 8 of their papers we have counts for
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Absence of absolutely continuous diffraction spectrum for certain S-adic tilings
Yasushi Nagai
Quasiperiodic tilings are often considered as structure models of quasicrystals. In this context, it is important to study the nature of the diffraction measures for tilings. In th…
On arithmetic progressions in non-periodic self-affine tilings
Yasushi Nagai, Shigeki Akiyama, Jeong-Yup Lee
We study the repetition of patches in self-affine tilings in R^d. In particular, we study the existence and non-existence of arithmetic progressions. We first show that an arithmet…
A new relation between geometric and dynamical properties of objects such as tilings and Delone sets
Yasushi Nagai
Let P be an object such as tiling, Delone set and weighted Dirac comb. There corresponds a dynamical system to P, called the corresponding dynamical system. Such dynamical systems…
Distribution of Patches in Tilings and Spectral Properties of Corresponding Dynamical Systems
Yasushi Nagai
A tiling is a cover of R^d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles that appears in tilings. From…