Seminar: "On typical rotation numbers for families of circle maps with singularities"

Professor Konstantin Khanin is a Raymond and Beverly Sackler Distinguished Lecturer in Pure Mathematics for the academic year 2023/2024.

Abstract

I shall discuss how one can define in a natural way the notion of typical rotation numbers for families of circle maps with singularities. This problem is related to a well known fact  that in the case of maps with singularities the set of parameters, corresponding to irrational rotation numbers, has zero Lebesgue measure.

Our approach is based on the hyperbolicity of renormalizations. 

I shall also discuss a natural setting for the Kesten theorem in the case of maps with singularities.