Flow views and infinite interval exchange transformations for recognizable substitutions

A flow view is the graph of a measurable conjugacy Φ between a substitution or S-adic subshift (Σ, σ, μ) and an exchange of infinitely many intervals in ([0, 1],F,m). The natural refining sequence of partitions of Σ is transferred to ([0, 1],m) using a canonical addressing scheme, a fixed dual substitution S∗, and a shift-invariant probability measure μ. On the flow view, τ is shown horizontally at a height of Φ(τ ). The IIET F is well approximated by exchanges of finitely many intervals, making numeric and graphic methods possible. The graphs of Fs show forms of self-similarity, a special case of which is proved. The spectral type of Φ ∈ L(Σ, μ), is of particular interest. As an example of utility, some spectral results for constant-length substitutions are included.

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