Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Smoothness of stable manifolds of circle renormalization

Talk by Paul Frigge

**Date:** 25.01.21 **Time:** 15.00 - 16.15 **Room:** Y27H28

In the setting of finitely smooth circle diffeomorphisms, the renormalization operator is not differentiable. In this lecture, I will discuss generalizable methods and techniques which allow us to prove that the topological classes of C^{4+ epsilon} circle diffeomorphisms with irrational rotation number of bounded combinatorial type are C^1 global smooth stable manifolds of renormalization. First I will explain how to extend renormalization to decomposition spaces, and construct a normed space of Mobius-Schwarzian decompositions on which the renormalization operator is jump-out hyperbolic. Using this notion, I will explain the construction of the local smooth stable manifolds in a neighborhood of the rigid rotations. This structure will then be globalized with the help of monotone families which transversely intersect the topological classes.