event
Thursday 03 Nov 2022: Equidistribution from self-conformal measures
Aleksi Pyorala - University of Oulu
Harrison 103 15:30-16:30
During recent years, the prevalence of normal numbers in natural subsets of the reals has been an active research topic in fractal geometry. The general idea is that in the absence of any special arithmetic structure, typical numbers in a given set should be normal, in every base. In our recent joint work with Balazs Barany, Antti Kaenmaki and Meng Wu we verify this for all self-conformal sets on the line. The result is a corollary of a uniform scaling property of self-conformal measures: roughly speaking, a measure is said to be uniformly scaling if the sequence of successive magnifications of the measure equidistributes, at almost every point, for a common distribution supported on the space of measures. Using machinery developed by Hochman and Shmerkin, dynamical properties of these distributions can be used to study prevalence of normal numbers in self-conformal sets.
