Analytic maps of parabolic and elliptic type with trivial centralisers

We prove that for a dense set of irrational numbers $α$, the analytic centraliser of the map $e^{2πi α} z+ z^2$ 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.

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