论文标题
具有共同迭代的两性理性地图
Bicritical rational maps with a common iterate
论文作者
论文摘要
令$ f $为$ d $ d $双政治理性映射，带有关键点集$ \ mathcal {c} _f $和临界值集$ \ mathcal {v} _f $。使用$ f^k $的甲板转换的组$ \ textrm {deck}（f^k）$，我们表明，如果$ g $是一张具有$ f $ tub $ f $ the $ \ nathCal {c} c} _f = \ nathcal {c} c} _g $ and $ f $ and $ f $ and $ f $和$ f $ and $ f $ and $ f $ and $ f $ and $ f $ and c} _g $ and nathcal calcal calcal calcal calcal { \ Mathcal {V} _g $。使用它，我们表明，如果两个偶数$ d $的两种双性理性地图共享一个迭代，那么他们共享第二个迭代，并且这两个地图都属于$ d $ d $ d $双政治理性地图的对称基因座。
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 which 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.
