Hurwitz对应的动力学度
Dynamical degrees of Hurwitz correspondences
摘要：
设$ϕ$是两球面的后临界有限分支覆盖。通过Koch的工作，由$ϕ$在Teichmüller空间上诱导的Thurston拉回映射下降到模空间$\mathcal{M}_{0,P}$的一个多值自映射--一个Hurwitz对应$\mathcal{H}_ϕ$.我们研究动态的赫维茨对应通过数值不变量称为动态度。我们证明了$\mathcal{H}_ϕ$的动力度序列总是非增的，并且该序列的行为受到$ϕ$在其后临界集的行为的约束.
英文摘要：
Let $ϕ$ be a post-critically finite branched covering of a two-sphere. By work of Koch, the Thurston pullback map induced by $ϕ$ on Teichmüller space descends to a multi-valued self-map --- a Hurwitz correspondence $\mathcal{H}_ϕ$ --- of the moduli space $\mathcal{M}_{0,P}$. We study the dynamics of Hurwitz correspondences via numerical invariants called dynamical degrees. We show that the sequence of dynamical degrees of $\mathcal{H}_ϕ$ is always non-increasing, and the behavior of this sequence is constrained by the behavior of $ϕ$ at and near points of its post-critical set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
