Currently displaying 1 – 5 of 5

Showing per page

Order by Relevance | Title | Year of publication

Embedding tiling spaces in surfaces

Charles HoltonBrian F. Martensen — 2008

Fundamenta Mathematicae

We show that an aperiodic minimal tiling space with only finitely many asymptotic composants embeds in a surface if and only if it is the suspension of a symbolic interval exchange transformation (possibly with reversals). We give two necessary conditions for an aperiodic primitive substitution tiling space to embed in a surface. In the case of substitutions on two symbols our classification is nearly complete. The results characterize the codimension one hyperbolic attractors of surface diffeomorphisms...

Structure of three interval exchange transformations I: an arithmetic study

Sébastien FerencziCharles HoltonLuca Q. Zamboni — 2001

Annales de l’institut Fourier

In this paper we describe a 2 -dimensional generalization of the Euclidean algorithm which stems from the dynamics of 3 -interval exchange transformations. We investigate various diophantine properties of the algorithm including the quality of simultaneous approximations. We show it verifies the following Lagrange type theorem: the algorithm is eventually periodic if and only if the parameters lie in the same quadratic extension of .

Page 1

Download Results (CSV)