An application of the degenerate Beltrami equation: quadratic polynomials with a Siegel disk

Liang Shen
2018 Annales Academiae Scientiarum Fennicae: Mathematica  
Let v(t) > 0 be a concave function such that´+ ∞ 1 1 tv(t) dt = +∞. If the continued fraction expansion of an irrational number 0 < θ < 1 has the coefficient a k which satisfies log 2 a k ≤ kv(k), k = 1, 2, · · · , the Julia set of e 2πiθ z + z 2 is locally connected and has Lebesgue measure zero. It extends the results of Petersen and Zakeri [10] .
doi:10.5186/aasfm.2018.4311 fatcat:bcuuwbr4ungwzorieukzdpbati