Analytic maps of parabolic and elliptic type with trivial centralisers

Artur Avila; Davoud Cheraghi; Alexander Eliad

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arXiv · 2003.13336

Analytic maps of parabolic and elliptic type with trivial centralisers

Artur Avila·Davoud Cheraghi·Alexander Eliad

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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.

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Artur Avila, Davoud Cheraghi, Alexander Eliad. 2020-03-30. Analytic maps of parabolic and elliptic type with trivial centralisers. https://arxiv.org/abs/2003.13336

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