Charles Holton

Learn More
Let s = (A, τ) be a primitive substitution. To each decomposition of the form τ (h) = uhv we associate a primitive substitution D [(h,u)] (s) defined on the set of return words to h . The substitution D [(h,u)] (s) is called a descendant of s and its associated dynamical system is the induced system (X h , T h ) on the cylinder determined by h . We show(More)
In this paper we present a detailed study of the spectral/ergodic properties of threeinterval exchange transformations. Our approach is mostly combinatorial, and relies on the diophantine results in Part I and the combinatorial description in Part II. We define a recursive method of generating three sequences of nested Rokhlin stacks which describe the(More)
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(More)
A substitution naturally determines a directed graph with an ordering of the edges incident at each vertex. We describe a simple method by which any primitive substitution can be modified (without materially changing the bi-infinite fixed points of the substitution) so that points in the substitution minimal shift are in bijective correspondence with(More)
Let A and F be finite sets and suppose for each a ∈ A we have a map φa : F → F. Suppose ω = ω1ω2ω3 . . . is a sequence in A which is ultimately primitive substitutive, i.e., a tail of ω is the image (under a letter to letter morphism) of a fixed point of a primitive substitution. We show that the induced sequence of iterates (φωn ◦φωn−1 ◦· · ·◦φω1) ∞ n=1 is(More)