日程安排
6月22日（周六）上午 |
时间 |
报告人 |
题 目 |
主持人 |
8:30-9:00 |
开幕式、合影 |
冯淑霞 （河南大学） |
9:00-9:45 |
沈维孝 (复旦大学) |
复动力系统中Thurston算法的若干应用 |
伍胜健 (北京大学) |
9:45-10:15 |
茶歇 |
10:15-11:00 |
连 增 (四川大学) |
Ergodic optimization theory for a class of discrete and continuous typical systems |
崔贵珍 (中国科学院数学与系统科学研究院) |
11:00-11:45 |
沈玉良 (苏州大学) |
VMO-Teichmuller space on the real line |
12:00 午餐 |
6月22日（周六）下午 |
时间 |
报告人 |
题目 |
主持人 |
2:00-2:45 |
刘立新 (中山大学) |
Almost isometries between Teichmüller spaces |
邱维元 (复旦大学) |
2:45-3:30 |
胡 骏 (美国纽约城市大学) |
Totally ramified (critical) rational maps |
3:30-4:00 |
茶歇 |
4:00-4:45 |
戎 锋 (上海交通大学) |
Some new invariants in local holomorphic dynamics |
高军杨 (中国矿业大学) |
4:45-5:30 |
凡石磊 (华中师范大学) |
Dynamical systems of p-adic rational maps |
6:30 晚餐 |
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6月23日（周日）上午 |
时间 |
报告人 |
题目 |
主持人 |
8:50-9:35 |
黄 文 (中国科学技术大学) |
熵和弱马蹄 |
漆毅 (北京航空航天大学(北京)) |
9:35-10:20 |
叶和溪 (浙江大学) |
Uniform bound for the number of common preperiodic points |
10:20-10:40 |
茶歇 |
10:40-11:25 |
许雷叶 (中国科学技术大学) |
Complexity and Sarnak conjecture |
王晓光 (浙江大学) |
11:25-12:10 |
张一威 (华中科技大学) |
Understanding physical mixing processes via transfer operator approach |
12:10 午餐 |
6月23日（周日）下午 |
2:00-5:30 |
自由讨论 |
报告题目及摘要
报告人：沈维孝（复旦大学）
题 目： 复动力系统中Thurston算法的若干应用
摘 要：Thurston在研究S^2上分支覆盖的动力系统性质时提出了一种算法。这个算法从指定的分支覆盖出发归纳构造出一列在适当的条件下收敛的有理函数。本报告讨论这个算法在横截性问题以及高次多项式族中重整算子研究中的应用。
报告人：连 增（四川大学）
题 目： Ergodic optimization theory for a class of discrete and continuous typical systems
摘 要：In this talk, I will report some recent development on ergodic optimization theory for a class of discrete and continuous typical systems, such as Anosov diffeomorphisms, Axiom A attractors, Axiom A flows. This is joint with Wen Huang, Xiao Ma, Leiye Xu and Yiwei Zhang.
报告人： 沈玉良（苏州大学）
题 目： VMO-Teichmuller space on the real line
摘 要：We introduce and discuss a new subclass of quasisymmetric homeomorphisms on the real line, which we call strongly symmetric homeomorphisms. Then we introduce a complex Banach manifold structure on the space of these strongly symmetric homeomorphisms with some normalized conditions.
报告人：刘立新（中山大学）
题 目： Almost isometries between Teichmüller spaces
摘 要：We prove that the Teichmüller space of hyperbolic surfaces with given boundary lengths equipped with the arc metric (resp. the Teichmüller metric ) is almost isometric to the Teichmüller space of punctured surfaces equipped with the Thurston metric (resp. the Teichmüller metric). This is joint work with Manman Jiang and Huiping Pan.
报告人：胡 骏（纽约城市大学）
题目： Totally ramified (critical) rational maps
摘要：By a totally ramified (critical) rational map we mean a rational map f satisfying that each pre-image of every critical value under f is a critical point. Furthermore, a totally ramified rational map f is said to be regularly ramified provided that for every critical value v, f has the same local degrees at all preimages of v. Up to pre- and post-compositions by Mobius transformations, regularly ramified rational maps correspond to quotient maps of finite Klein groups. A natural problem is to explore the existence of those totally ramified rational maps that are not regularly ramified. This question becomes more inspiring since it has been proved that one type of Fatou components can not appear for this type of rational maps. I will report the findings to this problem and state which type of Fatou components can not appear. These are joint works with Weiwei Cui and Yingqing Xiao respectively.
报告人：戎 锋 （上海交通大学）
题 目： Some new invariants in local holomorphic dynamics
摘 要：One of the main topics in local holomorphic dynamics is to generalize the “Leau-Fatou Flower Theorem” to higher dimensions. In this regard, local invariants are very important subjects. In this talk, we introduce several new invariants we obtained in recent years, ranging from “level one” to “level three”.
报告人： 凡石磊（华中师范大学）
题 目： Dynamical systems of p-adic rational maps
摘 要：Let $\phi\in \Q_p$ be a rational map with coefficients in $\Q_p$ the filed of $p$-adic numbers. We study the dynamical system induced by $\phi$ on the projective line $\P^{1}(\Q_p)$. When $\phi$ contains no recurrent critical point in $\Q_p$, we obtained the relation between the dynamical system $(\P^{1}(\Q_p), \phi)$ and $(\P^{1}(\C_p), \phi)$. For the PCF rational maps, the Julia sets are characterized by subshifts of finite of countable type. It is a joint work with Lingmin LIAO Hongmin NIE and Yuefei WANG.
报告人：黄 文（中国科学技术大学）
题 目： 熵和弱马蹄
摘 要：我们将介绍关于正熵系统与弱马蹄的一些进展。主要基于与Xu, Li，Lu和Ye的合作的几个工作。
报告人：叶和溪 （浙江大学）
题 目： Uniform bound for the number of common preperiodic points
摘 要：In this talk, we discuss the uniform boundedness for the number of common preperiodic points of quadratic polynomials with the form f(z)=z^2+c. This is a joint work with Laura DeMarco and Holly Krieger.
报告人：许雷叶 （中国科学技术大学）
题 目： Complexity and Sarnak conjecture
摘 要：In this talk, we intruduce Sarnak conjecture and Logarithmic version of Sarnak conjecture. It is showed that the Logarithmic version of Sarnak conjecture holds for all t.d.s with sublinear complexity. We also show the relationship between Logarithmic version of Sarnak conjecture and symbolic dynamical system with polynomial complexity.
报告人：张一威 （华中科技大学）
题 目： Understanding physical mixing processes via transfer operator approach
摘 要：Industrial and chemical mixing processes of various kinds occur throughout
nature and are vital in many technological applications.In the context of discrete
dynamical systems, the transfer operator approach has been shown as a powerful
tools from both theoretic and numerical viewpoint. In this talk, I will use a
toy model (i.e., the one dimensional stretch and fold map) as an example to
provide a brief introduction on the relationships between the spectral
properties of the associated transfer operator and the estimations of the
optimal mixing rate of the mixing process. Moreover, I will address how
the optimal mixing rate varies according to the stretch and fold map has
``cutting and shuffling'' behaviour (i.e., composing with a permutation).
If time permits, I will also talk about how to interpret this problem to
the eigenvalue estimations for the Random bi-stochastic matrices (free
probability theory) and the locations of poles of the dynamical zeta
function. These are joint works with Charles Bordenave, Nigel Byott,
Mark Holland and Yanqi Qiu.
