Analytic maps of parabolic and elliptic type with trivial centralisers

Abstract

We prove that for a dense set of irrational numbers $\alpha$, the analytic centraliser of the map $e^{2\pi i\alpha }z+z^2$ near $0$ is trivial. We also prove that some analytic circle diffeomorphisms in the Arnol’d family, with irrational rotation numbers, have trivial centralisers. These provide the first examples of such maps with trivial centralisers.