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Dynamical Systems seminar - Normal numbers and self-similar measures

Dates
Wednesday, May 4, 2022 - 14:00 to 15:00

Speaker: Simon Baker (University of Birmingham)

Abstract: A real number x is said to be normal in base b if the sequence (b^n x) is uniformly distributed modulo one. In this talk I will discuss a recent result which states that for a self-similar measure and an integer b, if the self-similar measure and b satisfy a suitable arithmetic assumption, then almost every x is normal in base b with respect to the self-similar measure. This is a joint work with Amir Algom and Pablo Shmerkin.