Separating Actions from Angles in Local Diffeomorphisms

Explore the intricacies of geometric normalization in analytic local diffeomorphisms of the plane during this 57-minute lecture by Alain Chenciner from the Institut des Hautes Etudes Scientifiques (IHES). Delve into the problem of normalization for local diffeomorphisms near weakly attracting elliptic fixed points with non-periodic rotation derivatives. Discover the concept of "geometric normalization" as an analytic local change of coordinates that transforms the local diffeomorphism to preserve the foliation by circles centered at the fixed point. Examine the works of Chenciner, David Sauzin, Shanzhong Sun, and Qiaoling Wei on the existence of normalizations and geometric normalizations in this advanced mathematical exploration.