Nicolas Gourmelon (Université de Bordeaux)

Explore a lecture on total renormalizations of perturbations of identity presented by Nicolas Gourmelon from Université de Bordeaux as part of the Simons Semester on Dynamics. Delve into the concept of total renormalization, defined as a transformation F: X → X conjugate to the first return of f to a domain ∆ whose orbit covers X, with the Rauzy-Veech induction on IETs given as an example. Discover the main result showing that any F ∈ Diff^∞_0(S^1 × M) is a total renormalization C^∞-close to identity maps, implying that all global dynamics exist arbitrarily C^∞-close to identity. Learn how this finding generalizes previous local results by Turaev, expanding our understanding of dynamical systems and their perturbations.