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 Arnold family, with irrational rotation numbers, have trivial centralisers. These provide the first examples of such maps with trivial centralisers.

13 Pages, No figures