TY - JOUR
T1 - An application of the degenerate Beltrami equation
T2 - Quadratic polynomials with a siegel disk
AU - Shen, Liang
N1 - Publisher Copyright:
© 2018 Annales Academiae Scientiarum Fennicae Mathematica.
PY - 2018
Y1 - 2018
N2 - 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 ak which satisfies log2 ak ≤ kv(k), k = 1, 2, · · ·, the Julia set of e2πiθz + z2 is locally connected and has Lebesgue measure zero. It extends the results of Petersen and Zakeri [10].
AB - 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 ak which satisfies log2 ak ≤ kv(k), k = 1, 2, · · ·, the Julia set of e2πiθz + z2 is locally connected and has Lebesgue measure zero. It extends the results of Petersen and Zakeri [10].
KW - Beltrami equation
KW - Mapping of finite distortion
KW - Siegel disk
UR - http://www.scopus.com/inward/record.url?scp=85042867206&partnerID=8YFLogxK
U2 - 10.5186/aasfm.2018.4311
DO - 10.5186/aasfm.2018.4311
M3 - Article
AN - SCOPUS:85042867206
SN - 1239-629X
VL - 43
SP - 267
EP - 277
JO - Annales Academiae Scientiarum Fennicae Mathematica
JF - Annales Academiae Scientiarum Fennicae Mathematica
ER -