Ergodic Theory of Interval Exchange Maps

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Extensive amenability and an application to interval exchanges (2015, result): “sidered by Katok and Stepin [KS67]. The systematic study started in the paper by Keane [Kea75], who introduced the terminology. For an introduction and account of the results, see the survey by Viana [Via06] or the book of Katok and Hasselblatt [KH95]. A basic question on IET was raised by Katok, na”
Non-ergodic Z-periodic billiards and infinite translation surfaces (2011, background): “Let us recall the definition of interval exchange transformations (IETs), with the presentation and notation from [40] and [41].”
Beyond substitutive dynamical systems: S-adic expansions (2013, methodology): “ a word that is the natural coding of an orbit of a k-iet. Rotations (for which the coding gives Sturmian words) are exactly the 2-iet. Here, we represent 3-iet words in an S-adic way and we refer to [133, 136] for more details on the theory of interval exchanges. In order to obtain an S-adic repres”