### All self-conformal measures are uniform scaling

Ergodic Theory and Dynamical Systems Seminar

3rd March 2022, 2:00 pm – 3:00 pm

Online via Zoom, Zoom

Scaling scenery is a useful tool for studying fine-structure properties of fractal objects. Measures for which the scaling scenery flows satisfy a strong statistical property, called uniform scaling, appear to be geometrically much more regular than general measures. Specific to self-conformal measures, the uniform scaling property has been proved to hold under the weak separation condition. In my talk, I will present a recent work, jointly with B.Barany, A.Kaenmaki and A.Pyorala, where we show that every self-conformal measure is uniform scaling, without assuming any separation conditions. If time permits, I will also present some applications of this result, for example, on prevalence of normal numbers in fractal sets.

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