论文标题
部分可观测时空混沌系统的无模型预测
Compositions of Belyi Maps and their Extended Monodromy Groups
论文作者
论文摘要
鉴于bely \uı映射$β\circγ：x \ rightarrow z $的组成，$β$的边缘之间的路径被扩展到形成回路，然后由$γ$提起。然后研究这些升降机，以了解$ z $中的循环如何在$β\Circγ$的边缘起作用，并在$ \ Mathop {\ Mathrm {mathrm {mon}}β\circγ\circγ\ linlhd \ mathop {\ mathrm {\ mathrm {montrm {mon}}γ\ wr \ nonop {在$π_{1}（z）$中抽取特定的bely \uı映射$γ$，并在$π_{1}（z）$中找到图像$γ$的单片表示。
Given a composition of Bely\uı maps $β\circ γ: X \rightarrow Z$, paths between edges of $β$ are extended to form loops, then lifted by $γ$. These liftings are then studied to understand how loops in $Z$ act on edges of $β\circ γ$, demonstrating the group operation in $\mathop{\mathrm{Mon}} β\circ γ\unlhd \mathop{\mathrm{Mon}} γ\wr \mathop{\mathrm{Mon}} β$. Abstracting away the specific Bely\uı map $γ$ and finding the image of $π_{1}(Z)$ in $π_{1}(Y) \wr \mathop{\mathrm{Mon}} β$ instead allows subsequently determining $\mathop{\mathrm{Mon}} β\circ γ$, for any $γ$, using only the monodromy representation of $γ$.
