威尼斯人

2018年“动力系统青年学者”小型研讨会

（会议时间：2018年12月8日至12月11日）

（会议地点：数学楼二楼学术报告厅）

会议日程

报告摘要

12月9日报告

1、报告题目：Exact solution and instability for geophysical trapped waves with centripetal forces

报告人：储继峰（上海师范大学）

摘要：The aim of this paper is to provide, in a \beta-plane approximation with centripetal forces, an explicit three-dimensional nonlinear solution for geophysical waves propagating at an arbitrary latitude, in the presence of a constant underlying background current. This solution is linearly un-stable when the steepness of the wave exceeds a specific threshold.

2、报告题目：Periodic solutions of nonlinear wave equation in inhomogeneous media

报告人：冀书关（东北师范大学）

摘要：In this talk, we consider the time periodic solutions of nonlinear wave equation with x-dependent coefficients. Such a model arises from the forced vibrations of an inhomogeneous string and the propagation of seismic waves in nonisotropic media. We shall talk about some recent results on the periodic solutions of the nonlinear wave equation in inhomogeneous media.

3报告题目：Smooth Hartman-Grobman Theorem for random and nonautonomous dynamical systems

报告人：张文萌（重庆师范大学）

摘要：Hartman-Grobman Theorem is one of the most basic results in the study of dynamical systems. However, for applications to homoclinic bifurcation, stability of mixing, Lorenz attractor and so on, one needs to improve the smoothness of topological conjugacy in the theorem.  In the talk, we present some recent results concerning the smooth Hartman-Grobman Theorem for random and nonautonomous dynamical systems.

4、报告题目：Exponential Dynamical Localization: Criterion and Applications

报告人：周麒（南京大学）

摘要：We give a criterion for exponential dynamical localization in expectation (EDL) for ergodic families of operators acting on $\ell^2(\Z^d)$. As applications, we prove EDL for a class of quasi-periodic long-range operators on $\ell^2(\Z^d)$. We also prove EDL for a class of quasi-periodic Schr\odinger operator on $\ell^2(\Z^d)$ with almost sharp dynamical localization exponent.  For supercritical almost Mathieu operators, we prove EDL with sharp dynamical localization exponent. This is joint work with J.You and L.Ge.

5、报告题目：Abelian by cyclic solvable group action on torus

报告人：薛金鑫（清华大学数学科学中心）

摘要：In this talk, we explain our joint work with Wilkinson and Hurtado on the rigidity problem of a class of solvable group called Abelian by cyclic groups acting on the torus. We get a complete classification in the 2D case up to topological conjugacy. We also get classification results in the higher dimensional case up to conjugacies of better regularity under extra assumptions.

6、报告题目：空间几乎周期KPP型非局部扩散方程的传播速度

报告人：梁兴（中国科学技术大学）

摘要：在这个报告中，我们将报告我们关于空间几乎周期KPP型非局部扩散方程的传播速度的工作。考虑的非局部扩散KPP方程解的水平集的长时间运动速度，这一速度刻画了解的时空动力学的基本结构，称之为传播速度。最一般的情况下，非局部扩散由直线上的概率测度描述。首先，利用偏微分方程中均质化的办法我们给出一般空间中传播速度的上下界估计。然后，利用动力系统的办法，我们证明：空间几乎周期传播速度上下界相同的充分必要条件是扩散概率的支撑生成的加法半群（R的自半群）在几乎周期函数Hull上的平移作用是遍历的。进一步，这一条件还等价于扩散概率的支撑不是几乎周期函数的某个频率生成加群的子集。

12月10日报告

7、报告题目：Special flow, weak mixing and complexity

报告人：黄文（中国科学技术大学）

摘要：In this talk, we will review some progress on Sarnak's conjecture. Finally, we will focus on the complexity of a special flow built over an irrational rotation of the unit circle and under a roof function on the unit circle. We construct a weak mixing minimal special flow with bounded topological complexity.

We also prove that if the roof function is $C^\infty$, then the special flow has  sub-polynomial topological complexity and the time one map meets the condition of Sarnak's conjecture.

8、报告题目：Invariant Cone Families in Infinite dimensional Dynamical Systems

报告人：王毅（中国科学技术大学）

摘要：In this talk, we will report some recent progress on the invariant cone families (ICF) in infinite-dimensional dynamical systems. For linear cocycles, we discuss the close relation of the ICF with Multiplicative Ergodic Theorem, dominated splitting (exponential separation), as well as Krein-Rutman Type Theorem. For nonlinear cocycles, we will show that ICF plays a key role in investi-gating the dynamics of several different kinds of differential equations.

9、报告题目：Topological characteristic factors along cubes of minimal systems

报告人：邵松（中国科学技术大学）

摘要：In this talk we study the topological characteristic factors along cubes of minimal systems. It is shown that up to proximal extensions the pro-nilfactors are the topological characteristic fac-tors along cubes of minimal systems. In particular, for a distal minimal system, the maximal $(d-1)$-step pro-nilfactor is the topological cubic characteristic factor of order $d$.

10、报告题目：双曲斜积系统的一些动力学结构

报告人：连增（四川大学）

摘要：双曲系统是动力系统领域最引人关注研究方向之一，然多数结果都集中在对确定系统的研究。近期，通过引入随机周期轨和随机马蹄的概念，我们对两类双曲斜积系统的动力学结构给出了一系列刻画。这是与吕克宁教授和黄文教授一起完成的