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

作者:Shen, Liang*
来源:Annales Academiae Scientiarum Fennicae-Mathematica, 2018, 43(1): 267-277.
DOI:10.5186/aasfm.2018.4311

摘要

Let v(t) > 0 be a concave function such that f(1)(+infinity) 1/tv(t) dt - +infinity. If the continued fraction expansion of an irrational number 0 < theta < 1 has the coefficient a(k) which satisfies l log(2) a(k) <= kv(k), k = 1, 2,..., the Julia set of e(2 pi i theta)z + z(2) is locally connected and has Lebesgue measure zero. It extends the results of Petersen and Zakeri [10].

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