Let $f:\widehat{\mathbb{C}}\to \widehat{\mathbb{C}}$ be a postcritically finite rational map, and let $\mathcal{Q}(\widehat{\mathbb{C}})$ be the space of meromorphic quadratic differentials on $\widehat{\mathbb{C}}$ with simple poles. We study the set of eigenvalues of the pushforward operator $f_{\ast }:\mathcal{Q}(\widehat{\mathbb{C}})\to \mathcal{Q}(\widehat{\mathbb{C}})$. In particular, we show that when $f:\mathbb{C}\to \mathbb{C}$ is a unicritical polynomial of degree $D$ with periodic critical point, the eigenvalues of $f_{\ast }:\mathcal{Q}(\widehat{\mathbb{C}})\to \mathcal{Q}(\widehat{\mathbb{C}})$ are contained in the annulus $\left\{\frac{1}{4D}<|\lambda |<1\right\}$ and belong to $\frac{1}{D}\mathbb{U}$ where $\mathbb{U}$ is the group of algebraic units.

中文翻译：

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Thurston运算符的特征值

让 $F：\widehat{\mathbb{C}}\to \widehat{\mathbb{C}}$ 成为后临界有限有理图，并让 $\mathcal{问}（\widehat{\mathbb{C}}）$ 是上亚纯二次微分的空间 $\widehat{\mathbb{C}}$简单的两极。我们研究前推运算符的特征值集$F_{\ast }：\mathcal{问}（\widehat{\mathbb{C}}）\to \mathcal{问}（\widehat{\mathbb{C}}）$。特别是，我们表明$F：\mathbb{C}\to \mathbb{C}$ 是度的单临界多项式 $d$ 带有周期性的临界点， $F_{\ast }：\mathcal{问}（\widehat{\mathbb{C}}）\to \mathcal{问}（\widehat{\mathbb{C}}）$ 包含在环中 $\left\{\frac{\mathrm{1个}}{4d}<|\lambda |<\mathrm{1个}\right\}$ 并属于 $\frac{\mathrm{1个}}{d}\mathbb{ü}$ 哪里 $\mathbb{ü}$ 是一组代数单位。