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Explore a 29-minute lecture by Olga Lukina from the Workshop on "Uniform Distribution of Sequences" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in April 2025. Delve into the fascinating world of infinite interval exchange transformations (IIETs), specifically focusing on rotated odometers obtained by pre-composing the von Neumann-Kakutani map with exchanges of finite intervals of equal length. Learn how these IIETs model first return maps of flows on translation surfaces with wild singularities. Discover the ergodic properties—including recurrence, discrepancy, diffusion coefficient, and ergodicity—of skew-products over rotated odometers through the lens of essential values theory and symbolic dynamical representations. This presentation covers joint research work conducted with Henk Bruin from the University of Vienna.
