An application of the degenerate Beltrami equation: Quadratic polynomials with a siegel disk

Liang Shen

doi:10.5186/aasfm.2018.4311

An application of the degenerate Beltrami equation: Quadratic polynomials with a siegel disk

Liang Shen^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 ak which satisfies log² ak ≤ 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].

Original language	English
Pages (from-to)	267-277
Number of pages	11
Journal	Annales Academiae Scientiarum Fennicae Mathematica
Volume	43
DOIs	https://doi.org/10.5186/aasfm.2018.4311
Publication status	Published - 2018

Keywords

Beltrami equation
Mapping of finite distortion
Siegel disk

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Shen, L. (2018). An application of the degenerate Beltrami equation: Quadratic polynomials with a siegel disk. Annales Academiae Scientiarum Fennicae Mathematica, 43, 267-277. https://doi.org/10.5186/aasfm.2018.4311

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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 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].",

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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].

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An application of the degenerate Beltrami equation: Quadratic polynomials with a siegel disk

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Keywords

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