动力系统与微分方程研讨会系列学术报告
报告题目： Strictly ergodic models and the pointwise convergence of non-conventional ergodic averages
报告人：叶向东教授（中国科大教授、杰青）
时间：2014.04.25 09：00-09:50
地点：金融工程中心报告厅
摘要：In this talk first I will survey the development related to the convergence of non-conventional ergodic averages.
Then I will present some new result on the pointwise convergence of non-conventional ergodic averages based on a joint work with Huang Wen and Shao Song.
报告题目： Singular nonlinear wave motion in mechanical and physical models: Dynamical System Method
报告人：张翼教授（浙江师范大学教授）
时间：2014.04.25 09:50-10:40
地点：金融工程中心报告厅
摘要： The investigation of the travelling wave solutions to nonlinear evolution equations plays an important role in the mathematical physics. In this talk, we will introduce dynamical system method, and understand the dynamical ideas in studying the travelling wave solutions of nonlinear wave equaitons. Some examples of nonlinear wave models are presented in detail.
题目：数学物理、算子谱理论和动力系统中的一些相关问题
报告人：尤建功教授（南京大学教授、杰青）
时间：2014.04.25 10:50-11:40
地点：金融工程中心报告厅
摘要： 拟介绍这三个领域交叉的一些问题以及问题间的相互联系；强调动力系统方法在数学物理和算子谱理论中的应用。
报告题目： On Dynamical Systems over Berkovich Space
报告人：王跃飞教授（科学院教授、杰青）
时间：2014.04.25 14:00-14:50
地点：金融工程中心报告厅
摘要： In recent years there is a considerable interest on the dynamics over non-Archimedean fields. Herman and Yoccoz's work in 1981 on Siegel’s linearization of non-Archimedean case was probably the first paper on the dynamical systems over non-Archimedean fields. The non-Archimedean fields behave topologically very badly, which are totally disconnected and not locally compact. In 1990 Berkovich introduced a new space, which is compact, path-connected and contains the non-Archimedean fields as dense subspaces in the sense of Gel'fand topology. In this talk we shall discuss the dynamics over Berkovich space, in comparison with the complex holomorphic dynamics. We shall talk about results on Julia sets and Fatou components of transcendental maps，Julia sets and its canonical measures of commuting rational maps，and minimal decomposition of linear rational maps.
报告人：庾建设教授（广州大学教授、杰青）
时间： 2014.04.25 15:30-16:20
地点： 金融工程中心报告厅
摘要：We are interested in the periodic solutions with a minimum period 4 to the delay differential equation x’(t) = -f(x(t - 1)), where f in C(R;R) is an odd function and g(x) = f(x)=x > 0 for x 6= 0. The well-known Kaplan-Yorke theorem shows that there is at least one such periodic solution if alpha= lim_{xto-infty}g(x)
and beta = lim_{xtoinfty}g(x) exist and sandwich pi/2, but the remaining cases were poorly understood. In this work, we completely resolve the remaining issues by identifying a local condition of f(x) over a finite interval that is essential
for the existence of this type of periodic solutions. We find several sufficient conditions for the existence of at least one or two such solutions whenalpha and beta are both larger (or smaller) than pi/2 or even when they are not well-defined. Finally, we put forward some Conjectures and Open Problems about the uniqueness and multiplicity of such periodic solutions.
报告题目：Furstenberg猜想与Cantor集的交
报告人：黄文教授（中国科大教授、杰青）
时间：2014.04.26 09:00-09:50
地点：金融工程中心报告厅
摘要：We will review some results on Furstenberg Conjecture and
discuss some related problems with intersections of Cantor sets.
discuss some related problems with intersections of Cantor sets.
报告题目： Almost everywhere convergence of ergodic series
报告人：范爱华教授（法国Amien大学教授、华中师范大学教授）
时间：2014.04.26 09:50-10:40
地点：金融工程中心报告厅
摘要：We consider ergodic series of the form $sum_{n=0}^infty a_n f(T^n x)$ where $f$ is an integrable function with zero mean value with respect to
a $T$-invariant measure $mu$. Under certain conditions on the dynamical system $T$, the invariant measure $mu$ and the function $f$, we prove thatthe series converges $mu$-almost everywhere if and only if $sum_{n=0}^infty |a_n|^2<infty$, and that in this case the sum of the convergent series is exponentially integrable and satisfies a Khintchine type inequality. We also prove that the system ${fcirc T^n}$ is a Riesz system if and only if the spectral measure of $f$ is absolutely continuous with respect to the Lebesgue measure and the Radon-Nikodym derivative is bounded from above as well as from below by a constant. We check the conditions for Gibbs measures $mu$relative to hyperbolic dynamics $T$ and for H"{o}lder functions $f$.
a $T$-invariant measure $mu$. Under certain conditions on the dynamical system $T$, the invariant measure $mu$ and the function $f$, we prove thatthe series converges $mu$-almost everywhere if and only if $sum_{n=0}^infty |a_n|^2<infty$, and that in this case the sum of the convergent series is exponentially integrable and satisfies a Khintchine type inequality. We also prove that the system ${fcirc T^n}$ is a Riesz system if and only if the spectral measure of $f$ is absolutely continuous with respect to the Lebesgue measure and the Radon-Nikodym derivative is bounded from above as well as from below by a constant. We check the conditions for Gibbs measures $mu$relative to hyperbolic dynamics $T$ and for H"{o}lder functions $f$.
报告题目：Hamilton-Jacobi方程的弱KAM理论
报告人：严军教授（复旦教授、杰青）
时间：2014.04.26 10:50-11:40
地点：金融工程中心报告厅
摘要：我们将Lagrange系统的弱KAM理论推广到“proper”Hamilton-Jacobi方程，通过引入变分解，解半群，采用动力系统的方法研究Hamilton-Jacobi方程粘性解的渐进行为。并探讨该方法在一般性Hamilton-Jacobi方程理论中进一步发展的可能性。
报告题目：拟线性偏微分方程的KAM及其应用
报告人：袁小平教授（复旦大学教授、杰青）
时间： 2014.04.26 14:00-14:50
地点：金融工程中心报告厅
摘要讨论不用频率分离性条件的无界扰动的KAM定理，并将其用于空间任意维的PDEs（包括拟线性的NLW、NLS和KP方程）而得到线性稳定的KAM环面。如时间允许，也介绍该定理的方法在Anderson localization和时滞微分方程中的应用。
报告题目：On the density of transverse homoclinic intersections for singular flows
报告人：甘少波教授（北京大学教授、杰青）
时间： 2014.04.26 15:30-16:20
地点： 金融工程中心报告厅
摘要：We will talk about a dichotomy result for three-dimensional singular flows.