论文标题
Mandelbrot集中完全是真实的点
Totally real points in the Mandelbrot Set
论文作者
论文摘要
最近，NoyTaptim和Petsche证明，$ f_c（z）的唯一完全真实的参数$ c \ in \ overline {\ mathbb q} $：= z^2+c $是有限的$ 0 $，$ -1 $和$ -2 $。在本说明中，我们表明唯一完全真实的参数$ c \ in \ overline {\ mathbb q} $，$ f_c $具有抛物线寄生循环为$ \ frac14 $，$ - \ frac34 $，$ - \ frac54 $和$ - \ - \ frac74 $。
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 $-\frac74$.
