Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 267-277

AN APPLICATION OF THE DEGENERATE BELTRAMI EQUATION: QUADRATIC POLYNOMIALS WITH A SIEGEL DISK

Liang Shen

Beijing Institute of Technology, School of Mathematics and Statistics
Beijing 100081, P.R. China; shenl 'at' bit.edu.cn

Abstract. 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

log²a_k ≤ kv(k), k = 1,2,...,

the Julia set of e^2πiθz+z2 is locally connected and has Lebesgue measure zero. It extends the results of Petersen and Zakeri [10].

2010 Mathematics Subject Classification: Primary 30C62, 30C65, 35J70.

Key words: Beltrami equation, mapping of finite distortion, Siegel disk.

Reference to this article: L. Shen: An application of the degenerate Beltrami equation: quadratic polynomials with a Siegel disk. Ann. Acad. Sci. Fenn. Math. 43 (2018), 267-277.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4311