Abstract:
We prove that one-parameter families of real germs of conformal diffeomorphisms tangent to the involution x -> -x are rigid in the parameter. We study the connection between the dynamics in the Poincar\’e and Siegel domains. Although repeatedly employed in the literature, the dynamics in the Siegel domain does not explain the intrinsic real properties of these germs. Rather, these properties are fully exploited in the Poincaré domain, where the fixed points are linearizable. However, a detailed study of the dynamics in the Siegel domain is of crucial importance. In this seminar we establish a connection between both points of view on the intersection of the Siegel normalization domains.