On an analytic approach to the Fatou conjecture

Genadi Levin

Genadi Levin

Fundamenta Mathematicae, Tome 173 (2002), p. 177-196 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $\sum_{n \geq 0} 1 / {(f ⁿ)}^{'} (c)$ 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.

Publié le : 2002-01-01

Zbl 0984.37046

EUDML-ID : urn:eudml:doc:282890

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Genadi Levin. On an analytic approach to the Fatou conjecture. Fundamenta Mathematicae, Tome 173 (2002) pp. 177-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm171-2-5/