会议日程安排

8:45-9:00   开幕式

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

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

10:30-10:45  茶歇

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

11:45-14:00  午餐（南苑宾馆）

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

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

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

17:15-18:00   自由讨论

18:00-20:00   晚餐（南苑宾馆）

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

11:15-12:00   报告11:关于退化低维不变环面的若干问题

12:30-14:30   午餐（南苑宾馆）

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

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

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

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.

Quasi-invariance of the determinantal point processes with Bergman kernels

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.

Positive homogeneousalmost periodicrotation number

TBA.

Combinatorial Structure of Amenable Groups and Applications

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

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

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.