Geodesic
On an analytic approach to the Fatou conjecture
Genadi Levin1
1 Institute of Mathematics The Hebrew University Givat Ram 91904, Jerusalem, Israel
Fundamenta Mathematicae, Tome 171 (2002) no. 2, pp. 177-196 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $\sum _{n\ge 0} {1/(f^n)'(c)}$ converges absolutely, then its sum is non-zero. In the proof we use analytic tools, such as integral and transfer (Ruelle-type) operators and approximation theorems.
DOI : 10.4064/fm171-2-5
Keywords: quadratic map generally complex plane sufficient conditions have measurable invariant linefields its julia set prove series sum converges absolutely its sum non zero proof analytic tools integral transfer ruelle type operators approximation theorems

Genadi Levin 1

1 Institute of Mathematics The Hebrew University Givat Ram 91904, Jerusalem, Israel 
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Genadi Levin. On an analytic approach to the Fatou conjecture. Fundamenta Mathematicae, Tome 171 (2002) no. 2, pp. 177-196. doi: 10.4064/fm171-2-5

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