# Does the boundary of immediate basin contain a fixed point?

Let $f$ be a rational map of degree $d\geq 2$, and $B$ is a simply connected immediate basin of an supper-attracting fixed point of $f$. I want to know whether there exists a fixed point of $f$ contained in $\partial B$. Any hint will be welcome! Or some similar result can be given!

• A fixed point that attracts supper? That would be interesting. – Gerry Myerson Mar 13 '18 at 11:23