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On an analytic approach to the Fatou conjecture

On an analytic approach to the Fatou conjecture

Let $f$ be a quadratic map (more generally, $f(z)=z^d+c$, $d>1$) of the complex plane. We give sufficient conditions for $f$ to have no measurable invariant linefields on its Julia set. We also prove that if the series $\sum _{n\ge 0} {1/(f^n)'(c)}$ conve