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arXiv · 2211.15725

Totally real points in the Mandelbrot Set

Xavier Buff·Sarah Koch
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Abstract

Recently, Noytaptim and Petsche proved that the only totally real parameters $c\in \overline{\mathbb Q}$ for which $f_c(z):=z^2+c$ is postcritically finite are $0$, $-1$ and $-2$. In this note, we show that the only totally real parameters $c\in \overline{\mathbb Q}$ for which $f_c$ has a parabolic cycle are $\frac14$, $-\frac34$, $-\frac54$ and $-\frac74$.

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Xavier Buff, Sarah Koch. 2022-11-28. Totally real points in the Mandelbrot Set. https://arxiv.org/abs/2211.15725

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