苏州大学动力系统12月小型研讨会 
                   2021 年 12 月 9 日— 12 月 10 日 
                         腾讯会议:899 644 359

12 月 9 日上午
题目:Measures of maximal u-entropy for maps that factor over Anosov 
报告人:杨帆(密歇根州立大学) 
时间:9:00-9:50 
摘要:In this talk, we will discuss the existence, uniqueness and statistical properties of the measures of maximal u-entropy for diffeomorphisms that factor over an Anosov diffeomorphism on a torus. Furthermore, we will use those measures to construct transverse measures of the unstable foliation, and prove that a natural dynamical averaging converges exponentially fast to the transverse measures. This is a joint work with Marcelo Viana, Raul Ures and Jiagang Yang.
题目:Asymptotic h-Expansiveness in Dynamical Systems 
报告人: 张国华 (复旦大学) 
时间:9:55-10:45 
摘要:In this talk I will review some properties and characterizations of asymptotic h-expansiveness in dynamical systems (including the integer group actions and general countable amenable group actions). This is based on joint works with Nhan-Phu Chung (Vietnam), Tomasz Downarowicz (Poland) and Wen Huang (China), Xiangdong Ye (China).
12 月 9 日下午
题目:Spin numbers: rotational Lyapunov exponents of Hamiltonian systems 
报告人: 邓艳霞(中山大学) 
时间:13:30-14:20 
摘要:Consider a symplectic diffeomorphism on a symplectic manifold. For any invariant probability measure, we introduce an invariant that measures the self-spinning of the invariant measure. This spin number in fact generalizes the Conley-Zehnder index for periodic points to invariant measures. We will also talk about its dependence on different choices of trivializations of the tangent bundle, and its applications to existence of periodic points. This is joint work with Zhihong Xia.
题目:A coupling approach in the computation of geometric ergodicity for stochastic dynamics 
报告人: 王式柔 (阿尔伯塔大学) 
时间:14:25-15:15 
摘要:This talk introduces a probabilistic approach to numerically compute geometric convergence rates in discrete or continuous stochastic systems. By choosing appropriate coupling mechanisms and combining them together, this approach works well in many settings, especially in high-dimensions. It is particularly observed that the rate of geometric ergodicity of a randomly perturbed system can, to some extent, reveal the degree of chaoticity of the unperturbed system. This is a joint work with Yao Li.
题目:An example in general group actions satisfying specification 
报告人: 任宪坤 (重庆大学) 
时间:15:20-16:10 
摘要:Specification property plays an important role in the study of dynamical systems. In this talk, we will introduce an example in general group actions satisfying specification.
题目:A generalized family of transcendental functions with one dimensional Julia sets 
报告人: 张旭 (山东大学威海分校) 
时间:16:15-17:05 
摘要:A generalized family of transcendental (non-polynomial entire) functions is constructed, where the Hausdorff dimension and the packing dimension of the Julia sets are equal to one. Further, there exist multiply connected wandering domains, the dynamics can be completed described, and for any nonnegative number s, there is a function taken from this family with the order of growth s.

12 月 10 日上午
题目:Isomorphism/KE of skew products: from Bernoulli to loosely Bernoulli 
报告人:董长光(马里兰大学) 
时间:9:00-9:50 
摘要:It’s well known that for Bernoulli systems, metric entropy is a complete invariant. That is, two Bernoulli systems are isomorphic iff they have the same metric entropy. However, isomorphism problem for dynamical systems apart from Bernoulli, becomes very complicate (and in fact not classifiable). In general, Kakutani equivalence (KE) may give much better description on both positive entropy and zero entropy systems. In this talk, we will focus on a very special systems, skew products. We will discuss recent results on the isomorphism/KE of such systems. Based on joint work with A. Kanigowski.
题目:The essential coexistence phenomenon in Hamiltonian dynamics 
报告人:胡虎翼(密歇根州立大学) 
时间:9:55-10:45 
摘要:A volume preserving dynamical system exhibits coexistence phenomenon if it consists of two invariant sets of positive volume, the regular part and chaotic part, on which the Lyapunov exponents are all zero and all nonzero respectively. Further, the system is ergodic on the chaotic part. If the regular set is nowhere dense, then we say that the system exhibits essential coexistence phenomenon. In this talk we construct an example of a Hamiltonian flow on a 4-dimensional smooth manifold which demonstrates essential coexistence of regular and chaotic dynamics on each energy surface. This is a joint work with Jianyu Chen, Yakov Pesin and Ke Zhang.
题目:On the integrability of Anosov endomorphisms 
报告人:史逸(北京大学) 
时间:10:50-11:40 
摘要:We show that an irreducible Anosov endomorphism on n-torus with one-dimensional stable bundle is special (it has invariant unstable bundle) if and only if it has spectrum rigidity in the stable bundle. This is a joint work with S. Gan and R. Gu.

12 月 10 日下午
题目:Multifractal analysis of singular hyperbolic attractors 
报告人:王晓东(上海交通大学) 
时间:13:30-14:20 
摘要:We study the multifractal analysis for singular hyperbolic attractors, including the geometric Lorenz attractors. For each singular hyperbolic homoclinic class whose periodic orbits are all homoclinically related and such that the space of ergodic probability measures is connected, we prove that: (i) level sets associated to continuous observables are dense in the homoclinic class and satisfy a variational principle; (ii) irregular sets are either empty or are Baire generic and carry full topological entropy. The assumptions are satisfied by C 1 -generic singular hyperbolic attractors and C r -generic geometric Lorenz attractors (r ≥ 2). The main technique we apply is the horseshoe approximation property.
题目:On arithmetically thick sets in Rd  
报告人: 丰德军 (香港中文大学) 
时间:14:25-15:15 
摘要:A compact set E in the d-dimensional Euclidean space is said to be arithmetically thick if there exists a positive integer n so that the n-fold arithmetic sum of E has non-empty interior. We give a sufficient condition to guarantee the arithmetic thickness. Moreover, we verify the arithmetic thickness for several classes of fractal sets, including all the self-similar sets and self-conformal sets that are not lying in a proper affine subspace. We also prove it for self-affine sets under mild assumptions. This is joint work with Yu-Feng Wu.
题目:Dynamics of Induced Maps on the Space of Probability Measures 
报告人: 邵华 (南京航空航天大学) 
时间:15:20-16:10 
摘要:Let f be a continuous self-map on a compact metric space X. f induces in a natural way a ⌃ map f on the space of all Borel probability measures on X. In this talk, we will present which of the topological properties of f (like transitivity, mixing, sensitivity, shadowing, and topological entropy, ⌃ etc.) are inherited by f and vice verse. In particular, we will discuss this topic in non-autonomous discrete system, which is generated by a sequence of continuous self-maps on X .This is a joint work with Guanrong Chen and Hao Zhu.
题目:Dynamics near a shear flow with Coriolis force 
报告人: 朱昊 (南京大学) 
时间:15:20-16:10 
摘要:In this talk, I will discuss the existence and properties of traveling waves near a shear flow when the Coriolis force is involved. For a class of flows, when the Coriolis parameter passes through a transitional point, the number of traveling wave families changes suddenly from finite to infinity. This indicates richer long time dynamics around the shear flow than the non-Coriolis case.