Structure of three-interval exchange transformations III: Ergodic and spectral properties

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Beyond substitutive dynamical systems: S-adic expansions (2013, background): “For S‐adic representations for 3‐iet see [2, 122], and for another type of induction for 3‐iet see also [77, 80, 81, 82].”
Continuous and Measurable Eigenfunctions of Linearly Recurrent Dynamical Cantor Systems (2003, background): “It is in general not true that all eigenvalues of a minimal dynamical system have a continuous eigenfunction as can be seen for some Toeplitz systems [3, 10] and for some interval exchange transformations [7].”
Structure of three-interval exchange transformations II: a combinatorial description of the tranjectories (2003, methodology): “This will be used in [ 14 ] to characterize possible eigenvalues of a three-interval exchange transformation and to obtain necessary and sufficient conditions for weak mixing, answering two questions posed by Veech in [22].”