Name
Title | ||
|---|---|---|
Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions |
Abstract | ||
|---|---|---|
The aim of this paper is to give an overview of recent results a bout 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 examples which correspond to algebraic parameters, are related to the iteration of one substitution, but we show that it is possible to treat arbitrary irrational examp les by using multidimensional continued fractions. We give some non-trivial applications to Diophantine approximation, numeration systems and tilings, and we expose the main unsolved questions. |
Year | Venue | Keywords |
|---|---|---|
2001 | DM-CCG | atomic surface,markov partitions,substitutions,fractal sets,translations on compact groups,numeration systems.,tilings,continued fraction,diophantine approximation,compact group |
Field | DocType | Citations |
Discrete mathematics,Combinatorics,Substitution tiling,Algebraic number,Algebra,Quasicrystal,Markov chain,Approximations of π,Pure mathematics,Mathematics,Diophantine approximation | Conference | 6 |
PageRank | References | Authors |
0.86 | 3 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pierre Arnoux | 1 | 34 | 5.39 |
| Valérie Berthé | 2 | 160 | 28.69 |
| Hiromi Ei | 3 | 12 | 2.48 |
| Shunji Ito | 4 | 14 | 3.12 |