Analytic maps of parabolic and elliptic type with trivial centralisers

Abstract

We prove that for a dense set of irrational numbers α, the analytic centraliser of the map e^{2πiα} z+ z2 near 0 is trivial. We also prove that some analytic circle diffeomorphisms in the Arnold family, with irrational rotation numbers, have trivial centralisers. These provide the first examples of such maps with trivial centralisers.