Bicritical Rational Maps With a Common Iterate

Abstract Let $f$ be a degree $d$ bicritical rational map with critical point set $\mathcal{C}_f$ and value $\mathcal{V}_f$. Using the group $\textrm{Deck}(f^k)$ of deck transformations $f^k$, we show that if $g$ is shares an iterate $f$, then $\mathcal{C}_f = \mathcal{C}_g$ $\mathcal{V}_f \mathcal{V}_g$. this, two maps even share iterate, they second both belong to symmetry locus maps.