Modul: MAT760 Ergodic theory and dynamical systems seminar

## Typical rotation numbers for families of circle maps with singularities

Talk by Prof. Dr. Konstantin Khanin

Speaker invited by: Prof. Dr. Corinna Ulcigrai

**Date:** 11.12.23 **Time:** 16.15 - 17.15 **Room:** Y27H25

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.''