将抛物理性质的有理映射与海克群配对
Mating parabolic rational maps with Hecke groups
AI总结：
研究证明具有抛物固定点且具有完全不变且单连通立即吸引盆地的有理映射可与海克群H_{d+1}配对，通过代数对应实现配对，验证了抛物版本的猜想。
摘要：
我们证明任何度数为d的有理映射，若其具有乘子为1的抛物固定点，并且具有完全不变且单连通立即吸引盆地，则可与海克群H_{d+1}配对，配对通过代数对应实现。这证实了在文献[BF1]中提出的关于有理映射与海克群配对的猜想的抛物版本。证明分为两步。第一步是构造一个压扁的多项式样映射，该映射是抛物有理映射与与海克群相关的抛物圆映射之间的配对。第二步是通过合适的分支覆盖将此压扁的多项式样映射提升为代数对应。
英文摘要：
We prove that any degree $d$ rational map having a parabolic fixed point of multiplier $1$ with a fully invariant and simply connected immediate basin of attraction is mateable with the Hecke group $H_{d+1}$, with the mating realized by an algebraic correspondence. This confirms the parabolic version of a conjecture on mateability between rational maps and Hecke groups made in \cite{BF1}. The proof is in two steps. The first is the construction of a pinched polynomial-like map which is a mating between a parabolic rational map and a parabolic circle map associated to the Hecke group. The second is lifting this pinched polynomial-like map to an algebraic correspondence via a suitable branched covering.
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