On an analytic approach to the Fatou conjecture

Genadi Levin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Let f be a quadratic map (more generally, f(z) = zd + 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 ∑n≥0 1/(fn)′(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.

Original languageAmerican English
Pages (from-to)177-196
Number of pages20
JournalFundamenta Mathematicae
Issue number2
StatePublished - 2002


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