主办单位：威尼斯人-威尼斯人娱乐场
苏州大学动力系统与微分方程研究中心
时间： 2018年11月30日至12月3日
地点： 数学楼二楼学术报告厅
会议日程
2018年11月30日（周五） | ||
12:00-18:00 | 报到 | |
18:00-20:00 | 晚餐 | |
2018年12月1日（周六） | ||
8:50-9:00 | 签到、开幕 | |
上午（第一场）：主持人黄文 | ||
报告时间 | 报告人 | 报告题目 |
9:00-9:30 | 张端智教授（南开大学） | Index estimation and brake orbits on Torus |
9:30-10:00 | 章梅荣教授（清华大学数学科学系） | 微分方程的解和宏观量 |
10:00-10:20 | 茶歇（拍照） | |
上午（第二场）：主持人张端智 | ||
10:20-10:50 | 程伟教授（南京大学） | Herglotz 变分原理及其应用 |
10:50-11:20 | 黄冠副教授（清华大学数学科学中心） | On the Integrability of Birkhoff Billiards |
11:20-11:50 | 黄文教授（中国科技大学） | Stable Sets and Chaos in Positive Entropy Systems |
12:00 | 午餐 | |
下午（第一场）：主持人严军 | ||
14:00-14:30 | 王林教授（清华大学数学科学中心） | Action minimizing methods for contact Hamiltonian systems and its applications |
14:30-15:00 | 崔小军教授（南京大学） | 二维 Lorentz 环面的动力学 |
15:00-15:30 | 宋玉林副教授（南京大学） | Gradient Estimates and Exponential Ergodicity for Mean-field SDEs Driven by Jump Processes |
15:30-15:50 | 茶歇 | |
下午（第二场）：主持人崔小军 | ||
15:50-16:20 | 严军教授（复旦大学） | 接触型 Hamilton-Jacobi 方程粘性解的存在性及其结构 |
16:20-16:50 | 袁小平教授（复旦大学） | Kolmogorov 定理的 Kolmogorov 证明及其应用 |
16:50-17:20 | 邵松教授（中国科技大学） | 动力系统中的幂零结构
|
17:30 | 晚餐 | |
2018年12月2日（周日） | ||
上午（第一场）：主持人薛金鑫 | ||
8:30-9:00 | 周敏副教授（南京大学） | 力学系统的不变柱面 |
9:00-9:30 | 窦斗副教授（南京大学） | Variational principles for metric mean dimensions |
9:30-10:00 | 代雄平教授（南京大学） | Universal dynamic compactification of topological dynamics and Veech's Free Theorem |
10:00-10:20 | 茶歇 | |
上午（第二场）：主持人窦斗 | ||
10:20-10：50 | 田学廷副教授（复旦大学威尼斯人 ） | Ergodic Average of Dynamical Orbits with Lebesgue Full Measure or Zero Measure |
10：50-11：20 | 朱朝锋教授（南开大学） | Normal formal of complex symplectic matrices |
11:20-11:50 | 史恩慧教授（苏州大学） | Topological conjugation classes of tightly transitive subgroups of $\text{Homeo}_{+}(\mathbb{S}^1)$ |
12:00 | 午餐 | |
下午分组讨论 | ||
第一组：地点(数学楼二楼学术报告厅)主持人赵云 | ||
1：20-2：00 | 糜泽亚（南京信息工程大学） | SRB measures for partially hyperbolic systems with multi 1D centers |
2：00-2：40 | 邹瑞（南京信息工程大学） | Periodic approximation of Lyapunov exponents for quasi-compact Banach cocycles |
2：40-3：20 | 王娟（上海工程技术大学） | The approximation of Lyapunov exponents by horseshoes for C1 diffeomorphisms with dominated splitting |
第二组：地点（数学楼307室） 主持人廖刚 | ||
1:00-1:30 | 胡锡俊（山东大学） | N体问题中的碰撞理论 |
1：30-2：00 | 薛金鑫（清华大学） | 在随机扰动下的某些动力系统量 |
2:00-2:30 | 瞿燕辉（清华大学） | Hausdorff维数谱的研究进展 |
2:30-3:00 | 谢践生（复旦大学） | 离散群上随机游走的渐近熵 |
2018年12月3日（周一） | ||
9：00-12：00地点：数学楼307自由讨论非一致双曲动力系统研究的最新进展 | ||
下午：地点(数学楼二楼学术报告厅)主持人Lloyd Simon | ||
2:00-3:00 | Shin KIRIKI (Tokai University) | Robust historic behavior of generic orbits for heterodimensional cycles |
3:00-4:00 | Yushi Nakano (Tokai University) | Persistent super-polynomial emergence for homoclinic tangencies |
4:00-5:00 | Zelerowicz Agnieszka (Pennsylvania State University) | EQUILIBRIUM MEASURES FOR SOME PARTIALLY HYPERBOLIC SYSTEMS
|
报告摘要
1、报告人：张端智教授（南开大学）
题目： Index estimation and brake orbits on Torus
摘要: In this talk, we will give an estimation on iL0 index with brake orbit boundary. As an application, we will introduce multiple existence of brake orbits of periodic reversible Hamiltonian systems on standard torus T2n. This is a joint work with Zhiping Fan.
2、报告人：章梅荣教授（清华大学数学科学系）
题目：微分方程的解和宏观量
摘要：以微分方程为研究对象，将阐述解、性质和宏观量是如何很强地依赖于方程中的无穷维参数的。通过特征值对于位势的这种依赖性质，我们将得到线性和非线性驻定薛定谔方程之间的联系。
3、报告人： 程伟教授（南京大学）
题目： Herglotz 变分原理及其应用
摘要： 我们将讨论 Herglotz 变分原理及其在切触型 Hamilton-Jacobi 方程中， 特别是在粘性解的表示公式以及非线性 discount 消失问题中的应用
4、报告人：黄冠副教授（清华大学数学科学中心）
题目：On the Integrability of Birkhoff Billiards
摘要：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 partially based on the joint works with Vadim Kaloshin and Alfonso Sorrentino.
5、报告人： 黄文教授（中国科技大学）
报告题目：Stable Sets and Chaos in Positive Entropy Systems
报告摘要：In this talk, I will present the chaotic phenomenon of a dynamical system with positive entropy. It is shown that a dynamical system has positive entropy if and only if it has a weak horseshoe.
Particularly, I will show that a Lorentz attractor has a weak horseshoe. Moreover, I will present the Hausdorff dimension and the chaotic behavior of stable sets and unstable sets in a C1-diffeomorphism system
with positive entropy. The lower bound of the Hausdorff dimension of
these stable sets and unstable sets is given in terms of the metric entropy and the largest Lyapunov exponent.
6、报告人：王林教授（清华大学数学科学中心）
题目：Action minimizing methods for contact Hamiltonian systems and its applications
摘要：Based on an implicit variational principle, I will introduce some fundamental results in Aubry-Mather theory and weak KAM theory for contact Hamiltonian systems. As its applications, I will show some properties of viscosity solutions to contact Hamilton-Jacobi equations with strictly decreasing dependence on the unknown function, for which the comparison theorem fails. This talk is based on a series of works joint with Kaizhi Wang and Jun Yan.
7、报告人： 崔小军教授（南京大学）
题目： 二维 Lorentz 环面的动力学
摘要： 我们讨论二维 Lorentz 环面上 eikonal 方程整体粘性解的存在性。我 们还将讨论有极点的二维 Lorentz 环面动力学的特殊性。
8、报告人： 宋玉林副教授（南京大学）
题目： Gradient Estimates and Exponential Ergodicity for Mean-field SDEs Driven by Jump Processes
摘要： In this talk, by using Malliavin calculus for Poisson functional, sharp gradient estimates for Mean-field SDEs driven by jump processes are established in non-degenerate case. Under a dissipative condition, exponential ergodicity is also obtained.
9、报告人： 严军教授（复旦大学）
题目： 接触型 Hamilton-Jacobi 方程粘性解的存在性及其结构
摘要： 给出接触型 Hamilton-Jacobi 方程粘性解的存在性的一个充分必要条 件，并给出粘性解的分层结构。
10、报告人： 袁小平教授（复旦大学）
题目： Kolmogorov 定理的 Kolmogorov 证明及其应用
摘要： KAM 理论中的 Kolmogorov 定理有两个证明，其一是 Arnold 的证明。 近年来人们发现 Kolmogorov 在 1954 年 ICM 中的原始证明概要也完全可行， 而且比 Arnold 的证明可以得到更多的结论。我们在这个 talk 中，首先介绍 Kolmogorov 的证明，然后给出若干新的应用。
11、报告人： 邵松教授（中国科技大学）
题目：动力系统中的幂零结构
摘要：在报告中，我们将介绍动力系统中的幂零结构及其应用。首先我们给出关于幂零系统的研究背景和它的一些基本动力学性质，然后介绍我们最近在这方面的一些工作。
12、报告人： 周敏副教授（南京大学）
题目： 力学系统的不变柱面
摘要： 对于自治 Hamilton 系统而言，如果某一能量面有一双曲周期轨，由 隐函数存在定理可知，存在双曲周期轨延拓到邻近等能量面。最近研究发 现，在通有条件下，在同宿轨附近也存在周期轨轨延拓，从而这些周期轨连同同宿轨构成一个带洞的二维柱面。
13、报告人：窦斗副教授（南京大学）
题目: Variational principles for metric mean dimensions
摘要：Gromov-Lindenstrauss-Weiss mean dimension is a meaningful quantity for large systems. In this talk, we will introduce our recent work on variational principles for metric mean dimensions.
14、报告人：代雄平教授（南京大学）
题目：Universal dynamic compactification of topological dynamics and Veech's Free Theorem
摘要：Let GRUC denote the right universal dynamic compactification of a Hausdorff topological group G with identity 1. Veech's Free Theorem (1977) asserts that if G is locally compact, then G acts freely on GRUC, i.e., tx≠x for all t\in G with t≠1 and x\in GRUC. We prove Veech's Free Theorem for any locally quasi-totally bounded Hausdorff topological group. This implies that the universal minimal flow is free of this class of topological group. Moreover, we show that there exists IP-recurrent points for any flow with compact Hausdorff phase space.
15、 报告人：田学廷副教授（复旦大学威尼斯人 ）
题目：Ergodic Average of Dynamical Orbits with Lebesgue Full Measure or Zero Measure
摘要：Palis' SRB conjecture and Takens' last problem both consider asymptotic behavior of ergodic average along dynamical orbits in the sense of Lebesgue measure. In this talk we discuss some related things, including:For partially hyperbolic systems, we show that Integrable expanding along central bundle of all physical-like measures (which exist naturally) imply that Lebesgue a.e. x, its time average corresponds to finite ergodic hyperbolic SRB measures;For C0 generic systems, we show that a set with Lebesgue full measure has zero topological entropy but a set with Lebesgue zero measure has full topological entropy;For C1 hyperbolic systems, we also show that a set with Lebesgue zero measure has full topological entropy.
16.报告人：朱朝锋教授（南开大学）
题目：Normal formal of complex symplectic matrices
摘要：The complete set of normal formal of complex symplectic matrices is given. For each basic normal form, the ultimated Krein numbers is calculated.
17、报告人：史恩慧教授（苏州大学）
题目：Topological conjugation classes of tightly transitive subgroups of Homeo+(S1)
摘要： Let Homeo+(S1) denote the group of orientation preserving homeomorphisms of the circle S1. A subgroup G of Homeo+(S1) is tightly transitive if it is topologically transitive and no subgroup H of G with [G: H]=\infty has this property;is almost minimal if it has at most countably many nontransitive points. In the paper, we determine all the topological conjugation classes of tightly transitive and almost minimal subgroups ofHomeo+(S1) which are isomorphic to Zn for any integer n≠2. This is a joint work with Hui Xu.
18、报告人：胡锡俊（山东大学）
题目：N体问题中的碰撞理论
摘要：我们将简单介绍N体问题的研究背景，然后介绍我们近期在碰撞指标理论，离心率接近1时的稳定性和双曲判别法的一些最新研究进展。
19、报告人：薛金鑫教授（清华大学）
题目：在随机扰动下的某些动力系统量
摘要：我们将介绍二维空间中关于某些保面积映射在随机扰动下的Lyapunov指数的最新研究结果，进一步介绍某些典型的二维映射在随机扰动下的Lyapunov指数和相关衰减的研究进展。最后对我们接下来将要开展的工作作一个简单的介绍。
20、报告人：瞿燕辉教授（清华大学）
题目：Hausdorff维数谱的研究进展
摘要：在本次报告中，我们将简单回顾分形几何研究的一些热点，特别是重分形分析——这是近几年分形几何领域的一个新的发展分支。我们将汇报一个在Thue-Morse哈密顿系统中关于Hausdorff维数谱的最新结果，同时对今后的工作计划做一个简单汇报。
21、报告人：谢践生教授（复旦大学）
题目：离散群上随机游走的渐近熵
摘要：在本次报告中，我们将介绍渐近熵的研究背景和意义，主要给同行介绍我们最近在离散群上的随机游走的渐近熵的范围。最后将介绍我们接下来的将开展的研究计划和预期成果。
22、报告人:糜泽亚（南京信息工程大学）
题目：SRB measures for partially hyperbolic systems with multi 1D centers
摘要：We prove the the existence of Sinai-Ruelle-Bowen measures for partially hyperbolic systems with multi 1 D centers. This is motivated by conjectures of Palis on the existence of physical (Sinai-Ruelle-Bowen) measures for global dynamics. This is a joint work with Yongluo Cao and Dawei Yang.
23、报告人：邹瑞（南京信息工程大学）
题目：Periodic approximation of Lyapunov exponents for quasi-compact Banach cocycles
摘要：We consider cocycles with values in the set of invertible bounded linear operators on a Banach space. We prove that if the base system has enough hyperbolicity, and the cocycles are quasi-compact, then the Lyapunov exponents of ergodic measures can be approximated by the exponents of measures on periodic orbits.
24、报告人:王娟（上海工程技术大学）
题目：The approximation of Lyapunov exponents by horseshoes for C1 diffeomorphisms with dominated splitting
摘要：Let f be aC1-diffeomorphism and \mu be a hyperbolic ergodic f-invariant Borel probability measure with positive measure-theoretic entropy. Assume that the Oseledec splitting
TxM = E1(x)
... Es(x)Es+1(x)... El(x)
is dominated on the Oseledec basin . We give extensions of Katok's Horseshoes construction. Moreover there is a dominated splitting corresponding to Oseledec subspace on horseshoes.
25、报告人：Shin KIRIKI (Tokai University)
题目：Robust historic behavior of generic orbits for heterodimensional cycles
摘要：The theme of this study is non-hyperbolic dynamical systems and historic behavior, where non-hyperbolic dynamical systems exactly refer to diffeomorphisms having heterodimensional cycles, and historic behavior means a phenomenon of the absence of Birkhoff time averages for orbits with respect to the Lebesgue measure. We show that arbitraily C1-close to any diffeomorphism f with co-index 1
heterodimensional cycles, there is a diffeomorphism which has a homoclinic class containing saddles of different indices and such that every orbit of generic subset of the homoclinic class has C1-robust historic behavior. This is joint work with Y. Nakano and T. Soma.
26、报告人：Yushi Nakano (Tokai University)
题目：Persistent super-polynomial emergence for homoclinic tangencies
摘要：Emergence at scale is the minimal number of probability measures to describe the orbit of the dynamics ``by means of statistics'' with precision . So, fast growth of emergence means irregular behaviour in the sense of Birkhoff’s ergodic theorem (called historic behaviour). It has recently been realized that a positive Lebesgue measure set of points with historic behaviour (persistently) appears for complicated dynamical systems, such as dynamical systems with heteroclinic connections or homoclinic tangencies. However, for all known results, growth rate of emergence is at most polynomial, and P. Berger conjectured that there are ``many'' dynamical systems with super-polynomial emergence. In this talk, I will give an affirmative answer to a version of Berger's conjecture: by arbitrary small perturbation of dynamical systems with persistent homoclinic tangencies, one can construct a positive Lebesgue measure set consisting of points with super-polynomial emergence. This is joint work with S. Kiriki and T. Soma.
27、报告人：Zelerowicz Agnieszka (Pennsylvania State University)
题目：EQUILIBRIUM MEASURES FOR SOME PARTIALLY HYPERBOLIC SYSTEMS
摘要：In this joint work with Vaughn Climenhaga and Yakov Pesin we study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle is integrable and nonexpanding, and show that every potential function satisfying the Bowen property has a unique equilibrium measure. Our method is to use tools from geometric measure theory to construct a suitable
family of reference measures on unstable leaves as a dynamical analogue of Hausdorff measure, and then show that the averaged pushforwards of these measures converge to a measure that has the Gibbs property and is the unique equilibrium measure.