会议 ID：384 2123 6785
会议密码：258036
入会链接：https://meeting.tencent.com/s/kwueQ763KNhQ
二、学术报告题目与摘要
The distribution of hyperbolic periodic points for some complete nonuniformly hyperbolic systems
曹永罗（苏州大学）
Abstract: In this talk, we will report some results about the distribution of hyperbolic periodic points for some complete nonuniformly hyperbolic systems. We also discuss equilibrium for sub-additive topological pressure of some special sub-additive potential.
有奇向量场的Palis弱稠密性猜测
甘少波（北京大学）
摘要：Palis弱稠密性猜测是指Morse-Smale系统与具有马蹄的系统的并集构成系统空间的一个开稠集。由于远离马蹄的系统一定远离同宿切，因而弱猜测的研究与远离同宿切的研究密切相关。在这个报告中我们证明，若X是远离同宿切的通有的d维向量场，C为X的一个非平凡的Lyapunonov稳定的链回复类，则C为同宿类。特别地，C中有马蹄。在三维时，这一结论蕴含弱稠密性猜测。
Entropies of commuting transformations on Hilbert space
历智明（西北大学）
Abstract: By establishing Multiplicative Ergodic Theorem for commutative transformations on a separable infinite dimensional Hilbert space, in this talk, we investigate Pesin’s entropy formula and SRB measures of a finitely generated random transformations on such space via its commuting generators.
Research on Pesin theory for systems with singularities
梁超（中央财经大学）
Abstract: In this talk, we investigate Pesin theory for systems with singularities and obtain some applications. This is a joint work with Ming Li.
Spectrum rigidity and dynamical Frobenius theorem for Anosov diffeomorphisms on 4-torus
史逸（北京大学）
Abstract: Let A be an irreducible Anosov automorphism on 4-torus. We show that for every f which is C2-close to A, every pair of f-invariant bundles are jointly integrable if and only if f admits spectrum rigidity in the f-invariant bundles dominated between them. This is a joint work with A. Gogolev.
Searching new phenomenon in uniformly hyperbolic systems
田学廷（复旦大学）
Abstract: One main goal in the study of dynamical systems is concerned with orbit structure, specifically long term or asymptotic behavior, for maps or flows. uniformly hyperbolic systems (such as Smale horseshoe and Anosov flow) are standard examples of complex or chaotic systems. Nowadays it is usual aiming to generalize the theory of uniform hyperbolicity to more general dynamics including nonuniform hyperbolicity and partial hyperbolicity. But in this talk we will revisit uniform hyperbolicity to make some new progress in searching the theory for uniformly hyperbolic systems, especially some collision phenomenon from topological perspective and probabilistic perspective including how one general orbit will go, how many types by classification and how about their dynamical complexity.
On the Patterson-Sullivan measures
王方（首都师范大学）
Abstract: In this talk, we will introduce the famous Patterson-Sullivan measures, which play important roles in the theory of geodesic flows. On negatively curved manifolds or rank-1 manifolds, the Patterson-Sullivan measures are closely related to the measure of maximal entropy (MME). We will show how to construct the Patterson-Sullivan measures, and exhibit some recent results about the Patterson-Sullivan measures and the MME.
Ergodic measure space of geometric Lorenz attractors
王晓东（上海交通大学）
Abstract: In this talk, we study the space of ergodic measures of geometric Lorenz attractors. We show that Cr-generically (r≥2), periodic measures are dense and hence the ergodic measure space is path-connected while Cr-densely, the singular measure is isolated in the ergodic measure space. Similar properties hold for C1 singular hyperbolic attractors of higher dimensions. This is a joint work with Yi Shi and Xueting Tian. We also show that every singular hyperbolic attractor, in particular the geometric Lorenz attractor, has the intermediate entropy property. This is a joint work with Ming Li, Yi Shi and Shirou Wang.
Unstable entropies and unstable pressure for random dynamical systems and endomorphisms
王昕晟（厦门大学）
Abstract: In this talk, we consider unstable metric entropy, unstable topological entropy, unstable pressure and their local versions for partially hyperbolic random dynamical systems and endomorphisms. Corresponding Shannon-McMillan-Breiman theorems are established, variational principles are also formulated, which give relationships between unstable metric entropy and unstable pressure (unstable topological entropy). And in the end, we will talk about entropy and pressure for noninvertible random dynamical systems via the preimage structure. This is a joint work with Weisheng Wu and Yujun Zhu.
Diffeomorphisms with a generalized Lipschitz shadowing property
文晓（北京航空航天大学）
Abstract: Shadowing property and structural stability are important dynamics with close relationship. Pilyugin and Tikhomirov proved that Lipschitz shadowing property implies the structural stability. Todorov gave a similar result that Lipschitz two-sided limit shadowing property also implies structural stability for diffeomorphisms. In this paper, we define a generalized Lipschitz shadowing property which unifies these two kinds of Lipschitz shadowing properties, and prove that if a diffeomorphism f of a compact smooth manifold M has this generalized Lipschitz shadowing property then it is structurally stable. The only if part is also considered. This is a joint work with Manseob Lee and Jumi Oh.
Ergodic optimization theory for a class of typical maps
许雷叶（中国科学技术大学）
Abstract: We consider ergodic optimization problem for a class of dynamical systems, including Axiom A attractors, Anosov diffeomorphisms and uniformly expanding maps or flows. We show that for generic observables, including Holder function spaces and C1 function space, the minimizing measure is unique and supports on a periodic orbit.
Lyapunov optimizing measures and periodic measures for C2 expanding maps
杨大伟（苏州大学）
Abstract: We consider the typical Lyapunov minimizing measures for expanding self-maps on the circle. The main result obtained in this paper is that there exists an open and dense subset P of all C2 expanding self-maps such that for each T∈P, the Lyapunov minimizing measures of T are uniquely supported on a periodic orbit. This answers a conjecture of Jenkinson-Morris positively. This is a joint work with W. Huang and L. Xu.
Arithmetic version of Anderson localization via reducibility
尤建功（南开大学）
Abstract: The arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given by Jitomirskaya for the almost Mathieu operators (AMO). Later, the result was generalized by Bourgain-Jitomirskaya to a class of one dimensional quasi-periodic long-range operators. In this paper, we propose a novel approach based on an arithmetic version of Aubry duality and quantitative reducibility which enables us to prove the same result for the class of quasi-periodic long-range operators in all dimensions. This is a joint work with Lingrui Ge.
Anosov-Katok construction for quasiperiodic cocycles
周麒（南开大学）
Abstract: In this talk, we will talk about Anosov-Katok construction for quasiperiodic SL(2, R) cocycles, and its various dynamical applications, for example, the continuity of the Lyapunov exponent, the growth of the cocycles.
SRB measures for pointwise hyperbolic systems on open regions
周云华（重庆大学）
Abstract: A diffeomorphism f: M→M is pointwise partially hyperbolic on an open invariant subset N⊆M if there is an invariant decomposition TNM=Eu⊕Ec⊕Es such that Dxf is strictly expanding on Eu(x) and contracting on Es(x) at each x∈N. We show that under certain conditions f has unstable and stable manifolds, and admits a finite or an infinite u-Gibbs measure 𝜇. If f is pointwise hyperbolic on N, then 𝜇 is an SRB measure or an infinite SRB measure. As applications, we show that some almost Anosov diffeomorphisms and gentle perturbations of Katok's map have the properties. This is a joint work with Jianyu Chen and Huyi Hu.