Analytic centralisers of quadratic germs and the Brjuno dichotomy

Wen Si

For $Q_{\alpha }(z)=e^{2\pi i\alpha }z+z^2$ with $\alpha$ irrational, we prove that the analytic centraliser of $Q_{\alpha }$ is trivial whenever $Q_{\alpha }$ is not analytically linearizable. Together with the quadra…