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                                                            会议日程安排

第一天:12月1日

 

会议报到

地点:南京大学数学系308报告厅

 

第二天:12月2日

 

上午  主席:      徐君祥

 

8:45-9:00   开幕式      

报告人:    王奕倩

 

9:00-9:45   报告1:On dimension of spectrum of Schrodinger oper- ator with periodic doubling potential

报告人:    刘庆晖(北京理工大学)

 

9:45-10:30  报告2:The Stability of Full Dimensional KAM tori for Nonlinear Schrodinger equation

报告人:    丛洪滋(大连理工大学)

 

10:30-10:45  茶歇

 

10:45-11:30 报告3:Invariant measures for Interval Maps with Critical Points and Singularities

报告人:    崔鸿飞(中国科学院武汉物理与数学研究所)

 

11:45-14:00  午餐(南苑宾馆)

 

下午  主席:      刘庆晖

14:00-14:45  报告4:随机扰动动力系统的Lyapunov指数和相关性衰减

报告人:    薛金鑫(清华大学)

 

14:45-15:30  报告5:Quasi-invariance of the determinantal point processes with Bergman kernels

 报告人:    邱彦奇(中科院数学所)

 

15:30-15:45  茶歇

 

15:45-16:30  报告6:无焦点流形上测地流的动力学

报告人:    王方(首都师范大学)

 

16:30-17:15  报告7:Positive homogeneous,almost periodic,rotation number

报告人:      周喆(中科院应用数学研究所)

 

17:15-18:00   自由讨论

 

18:00-20:00   晚餐(南苑宾馆)

 

第三天:12月3日

 

上午  主席:        耿建生

 

 8:45-9:30     报告8:Combinatorial Structure of Amenable Groups and Applications

 报告人:      张国华(复旦大学)

 

 9:30-10:15   报告9:Local stable sets for positive entropy $C^1$ diffeomorphisms

 报告人:      高睿(四川大学)

 

10:15-10:30   茶歇

 

10:30-11:15   报告10:On the integrability of Birkhoff Billiards

报告人:      黄冠(清华大学)

 

11:15-12:00   报告11:关于退化低维不变环面的若干问题

报告人:      徐君祥

   

12:30-14:30   午餐(南苑宾馆)

 

下午  主席:        周麒

 

14:30-17:00   自由讨论

 

17:30-19:30   晚餐(南苑宾馆),会议闭幕

 

 

                                                                    报告信息

On dimension of spectrum of Schrodinger operator with periodic doubling potential

刘庆晖(北京理工大学)

By study iteration of germ, it is proved that the Hausdorff dimension of spectrum of Schrodinger operator with Thue-Morse potential has common positive low bound for all coupling. We study the property of related iteration of germ for Schrodinger operator with periodic doubling potential.

 

 The Stability of Full Dimensional KAM tori for Nonlinear Schrodinger equation

丛洪滋(大连理工大学)

In this paper, it is proved that the full dimensional invariant tori obtained by Bourgain [J. Funct. Anal., \textbf{229} (2005), no. 1, 62-94.] is stable in a very long time for 1D nonlinear Schr\"{o}dinger equation with periodic boundary conditions.

 

Invariant measures for Interval Maps with Critical Points and Singularities

崔鸿飞(中国科学院武汉物理与数学研究所)

For a class of piecewise $C^2$ interval maps with critical points and singularities (may with discontinuities at critical points and singularities), under a mild condition on the growth of the derivative on critical orbits and the recurrence of such orbits to the critical/singular set, we prove the existence and superpolynomial decay of correlation of an invariant probability measure which is absolutely continuous with respect to Lebsegue measure.

 

随机扰动动力系统的Lyapunov指数和相关性衰减

薛金鑫(清华大学)

动力系统中一些重要的映射包括标准映射,和Henon映射在大参数的情况,解析的研究其动力学行为极端困难。我们考虑在这种系统上加一个随机的小扰动,就可以相对容易的得到动力学信息,包括定量的Lyapunov指数估计,以及指数式相关性衰减的估计。 我们也给出对所需的随机扰动的大小的下界估计。 我们的结果解释了对以上映射的数值计算总是有正的Lyapunov指数,和指数相关性衰减,因为随机扰动可以看成机器误差。 这是跟Lai-Sang Young和Alex Blumenthal合作的结果。

 

Quasi-invariance of the determinantal point processes with Bergman kernels

邱彦奇(中科院数学所)

Determinantal point processes are probability measures on the space of configurations. I will briefly introduce the general theory and report the quasi-invariance of determinantal point processes related to Bergman spaces. The talk is based on joint works with Alexander Bufetov, Alexander Bufetov and Shilei Fan.

 

无焦点流形上测地流的动力学

王方(首都师范大学)

 

Positive homogeneousalmost periodicrotation number

周喆(中科院应用数学研究所)

TBA.

 

Combinatorial Structure of Amenable Groups and Applications

张国华(复旦大学)

称可数离散群$G$为amenable的,如果具有$G$的非空有限子集序列$\{F_n: n\in \mathbb{N}\}$使得$\lim_{n\rightarrow \infty} \frac{\# (g F_n\Delta F_n)}{\# (F_n)}= 0$对所有的$g\in G$都成立,其中$\# (A)$表示集合$A$的基数。我们通过研究amenable群的组合结构来证明:一定存在零维的具有零熵的自由$G$系统。这个工作是同波兰数学家Tomasz Downarowicz和Dawid Huczek一起合作完成的。注意到,是否具有符号$G$系统也满足这样的性质,这个问题至今尚未解决。

 

Local stable sets for positive entropy $C^1$ diffeomorphisms

高睿(四川大学)

In this talk, we consider the local stable/unstable sets for $C^1$ dynamical systems on either a compact manifold or some compact invariant set in a Banach space. Assuming that such a dynamical system admits an ergodic invariant measure with positive entropy, a lower bound of the Hausdorff dimension for the local stable/unstable sets is given in terms of the measure-theoretical entropy and the maximal Lyapunov exponent. This is a joint work with Shilin Feng, Wen Huang and Zeng Lian.

 

On the integrability of Birkhoff Billiards

黄冠(清华大学)

The famous Birhkhoff conjecture claims that all the integrable billiard systems are those induced by ellipses. I will review recent progresses in the study of Birhkhoff conjecture. This talk is partailly based on the joint works with Vadim Kaloshin and Alfonso Sorrentino.

 

关于退化低维不变环面的若干问题

徐君祥(东南大学)

主要介绍近可积哈密顿系统退化双曲和椭圆低维环面在小扰动下的保持性问题,介绍已经取得的一些结果,以及有待解决的问题和关键性困难。

 

Date icon 2017-11-28