Zoom, Online seminar
(線上演講 Zoom)
Normal Numbers in Self-conformal Sets
Aleksi Pyörälä (University of Oulu)
Abstract
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, almost all numbers in a given set should be normal, in every base. In our recent joint work with Balázs Bárány, Antti Käenmäki and Meng Wu we verify this for self-conformal sets on the line. The result is a corollary of a uniform scaling property of self-conformal measures which I will also discuss: 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 measure on the space of measures.
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