Analytic maps of parabolic and elliptic type with trivial centralisers (Q2693527)

Summary: 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.