Abstract:

Lef $f$ be a function with two critical values and no asymptotic values, which weassume to have no parabolic periodic orbits. We also assume that periodic rays land.Fix $p\; >=1$ and let $F=fp$. We prove that every two fixed points of $F$ which are notlanding points of fixed rays of $F$, can be separated by a pair of fixed rays of $F$ which land at a common point.As a corollary we obtain, for example, that there are no Cremer periodic points on the boundary of Fatou components.