12 citations · 65 across the 36 of their papers we have counts for
15 papers · 1 filter
The natural extension of the -transformation
Shigeki Akiyama, Hiromi Ei, Hiroaki Ito
We give a concrete construction of a natural extension of -transformation when is greater than the golden mean. Our construction relies on its Markov diagram and the eige…
Pure Discrete Spectrum and Regular Model Sets in Unimodular Substitution Tilings on R^d
Dong-il Lee, Shigeki Akiyama, Jeong-Yup Lee
We consider primitive substitution tilings on R^d whose expansion maps are unimodular. We assume that all the eigenvalues of the expansion maps are algebraic conjugates with the sa…
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…
Generic point equivalence and Pisot numbers
Shigeki Akiyama, Hajime Kaneko, Dong Han Kim
Let be an integer or generally a Pisot number. Put on and let be a piecewise linear transformation whose slopes have the form $\…
Spiral Delone sets and three distance theorem
Shigeki Akiyama
We show that a constant angle progression on the Fermat spiral forms a Delone set if and only if its angle is badly approximable.
Yet another characterization of the Pisot substitution conjecture
Paul Mercat, Shigeki Akiyama
We give a sufficient geometric condition for a subshift to be measurably isomorphic to a domain exchange and to a translation on a torus. And for an irreducible unit Pisot substitu…