Analytic maps of parabolic and elliptic type with trivial centralisers

Artur Avila, Davoud Cheraghi, Alexander Eliad

21/4/20 Published in : arXiv:2003.13336

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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Statistical Mechanics

Invariant graphs and spectral type of Schrödinger operators

Delocalization transition for critical Erdős-Rényi graphs