Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions

Autor: Pierre Arnoux, Valerie Berthe, Hiromi Ei, Shunji Ito

Publikováno v: Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings vol. AA,..., Iss Proceedings (2001)

The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution. The simplest exa

Externí odkaz: https://doaj.org/article/36fe831d83c9414f9f028d051eb049d8

On the construction of the natural extension of the Hurwitz complex continued fraction map

Autor: Hitoshi Nakada, Rie Natsui, Shunji Ito, Hiromi Ei

Publikováno v: Monatshefte für Mathematik. 188:37-86

We consider the Hurwitz complex continued fraction map associated to the Gaussian field $${\mathbb {Q}}(i)$$ . We characterize the density function of the absolutely continuous invariant measure for the map associated to the Hurwitz continued fractio

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e21a944292ed168ec79717443438d95c
https://doi.org/10.1007/s00605-018-1229-0

Stepped surfaces and Rauzy fractals induced from automorphisms on the free group of rank 2

Autor: Hiromi Ei

Publikováno v: Theoretical Computer Science. 528:57-78

From irreducible unimodular Pisot substitutions of rank 2, we can construct the discrete approximations of the lines, the so-called stepped surfaces, and moreover, we obtain Rauzy fractals as geometric realizations of the symbolic dynamical systems.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4f5c168292874819aa2019c1fa4900b9
https://doi.org/10.1016/j.tcs.2014.02.004

On substitution invariant Sturmian words: an application of Rauzy fractals

Autor: Hiromi Ei, Shunji Ito, Valérie Berthé, Hui Rao

Publikováno v: RAIRO-Theoretical Informatics and Applications (RAIRO: ITA)
RAIRO-Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2007, 41, pp.329-349

Sturmian words are infinite words that have exactly n + 1 factors of length n for every positive integer n. A Sturmian word s�,� is also defined as a coding over a two-letter alphabet of the orbit of the pointunder the action of the irrational ro

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9342b1a1fa0b262846124eab9d48e639
https://doi.org/10.1051/ita:2007026

Tilings of a Riemann surface and cubic Pisot numbers

Autor: Fumihiko Enomoto, Hiromi Ei, Shunji Ito, Maki Furukado

Publikováno v: Hiroshima Math. J. 37, no. 2 (2007), 181-210

Using the reducible algebraic polynomial \(x^{5} - x^{4}-1 = \left( x^{2}-x + 1 \right) \left( x^{3} - x - 1 \right),\) we study two types of tiling substitutions $\tau^*$ and $\sigma^*$: $\tau^*$ generates a tiling of a plane based on five prototile

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e33a1d3d15ddb60a4b183713fd9715f
https://doi.org/10.32917/hmj/1187916318