Report
Thurston's pullback map, invariant covers, and the global dynamics on curves
| العنوان: | Thurston's pullback map, invariant covers, and the global dynamics on curves |
|---|---|
| المؤلفون: | Bonk, Mario, Hlushchanka, Mikhail, Lodge, Russell |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Mathematics - Complex Variables, 37F10, 37F20 |
| الوصف: | We consider rational maps $f$ on the Riemann sphere $\widehat {\mathbb{C}}$ with an $f$-invariant set $P\subset \widehat {\mathbb{C}}$ of four marked points containing the postcritical set of $f$. We show that the dynamics of the corresponding Thurston pullback map $\sigma_f$ on the completion $\overline{\mathcal{T}_P}$ of the associated Teichm\"uller space $\mathcal{T}_P$ with respect to the Weil-Petersson metric is easy to understand when $\overline{\mathcal{T}_P}$ admits a cover by sets with good combinatorial and dynamical properties. In particular, the map $f$ has a finite global curve attractor in this case. Using a result by Eremenko and Gabrielov, we also show that if $P$ contains all critical points of $f$ and each point in $P$ is periodic, then such a cover of $\overline{\mathcal{T}_P}$ can be obtained from a $\sigma_f$-invariant tessellation by ideal hyperbolic triangles. Comment: 12 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2411.00732 |
| رقم الانضمام: | edsarx.2411.00732 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |