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