# 在新加坡的这五年—学术篇

### 基础书籍：

(1) Complex Analysis, 3rd Edition, Lars V. Ahlfors

(2) Complex Analysis, Elias M. Stein

(1) Lectures on Riemann Surfaces (GTM 81), Otto Forster

(2) Lectures on Quasiconformal Mappings, Lars V. Ahlfors

(1) Real Analysis and Complex Analysis, Rudin

(2) Real Analysis, Elias M. Stein

### 专业书籍：

(1) One Dimensional Dynamics, Welington de Melo & Sebastian VanStrien

(2) Mathematical Tools for One-Dimensional Dynamics (Cambridge Studies in

Advanced Mathematics), Edson de Faria / Welington de Melo

(3) Dynamics in One Complex Variable, John Milnor；Milnor 的教材总是写的清晰明确，容易上手，推荐初学者可以读这本书。

(4) Complex Dynamics, Lennart Carleson；Carleson 的教材偏向于分析学，读起来其实也有点难度，还是读 Milnor 的教材相对容易。

(5) Complex Dynamics and Renormalization, Curtis T. McMullen；McMullen 的书适合当做查阅，也不太适合从头到尾读下去。

(6) Renormalization and 3-Manifolds Which Fiber over the Circle, Curtis T. McMullen

(7) Iteration of rational functions (GTM 132), Alan F. Beardon

(8) An Introduction to Ergodic Theory (GTM 79), Walters Peter

### 论文

Question. 是否存在 $\ell\geq 4$ 的偶数和复数 $c\in\mathbb{C}$ 使得 $f(z)=z^{\ell}+c$ 的 Julia 集合 $J(f)$ 是正测度？

1. Combinatorics, geometry and attractors of quasi-quadratic maps，Pages 345-404 from Volume 140 (1994), Issue 2 by Mikhail Lyubich

2. Wild Cantor attractors exist，Pages 97-130 from Volume 143 (1996), Issue 1 by Hendrik Bruin, Gerhard Keller, Tomasz Nowicki, Sebastian van Strien

3. Quadratic Julia sets with positive area，Pages 673-746 from Volume 176 (2012), Issue 2 by Xavier Buff, Arnaud Chéritat

4. Polynomial maps with a Julia set of positive measure，Nowicki, Tomasz, and Sebastian van Strien，arXiv preprint math/9402215(1994).

### 参考资料：

1. 科研这条路
2. 维基百科：Julia 集合

Advertisement