确定与随机动力系统论坛（大连2018）

由大连理工大学数学科学学院组织承办的“确定与随机动力系统论坛”（大连2018）定于2018年8月23日-8月26日在辽宁省大连市举行。

会议地点：创新园大厦A1101

联系人：王跃飞

法国Picardie大学 范爱华

报告题目：Dvoretzky covering with non-uniformly distributed centers

报告摘要：Let &micro; be a Borel probability measure on the circle T := R/Z ≡ [0,1]. Suppose that we are given a sequence of i.i.d. random variables (ξ)n≥1 having &micro; as probability law and a sequence of positive numbers (ℓn)n≥1 with 0 < ℓn< 1. Denote In:= (ξn− ℓn/2, ξn+ ℓn/2), the random interval of length ℓn and centered at ξn. Under what condition on &micro; and on (ℓn) have we

P(T = limsup In)= 1?

When &micro; is the Lebesgue measure, it is the famous Dvoretzky covering problem and a complete solution is known (L. Shepp). We will give some partial answers when &micro; is not the Lebesgue measure.

华中师范大学 凡石磊

报告题目：The bound for the number of preperiodic points quadratic rational polynomials

报告摘要：Arithmetic Dynamics is the study of number theoretic properties of dynamical systems. The transposition of classical results from arithmetic geometry and the theory of Diophantine equations to the setting of discrete dynamical systems leads to a host of new and interesting questions. Let \psi be a morphism on the projective line over a number field. Then the number of preperiodic points is finite.  Morton and Silverman conjecture that there is a uniform bound for the number of preperiodic points. It is still open even for the family of rational quadratic polynomials. I will introduce our recent progress for quadratic polynomials. This is a joint work with Ye Hexi.

清华大学丘成桐数学中心 韩勇

报告题目: About the convergence of harmonic explorer with alternating boundary conditions

报告摘要: In the first part ,we will give an introduction to SLE process and its variants.  And in the second part, the harmonic explorer model with alternating boundary conditions on the triangular lattice and its convergence to SLE(\kappa, \rho) processes will be issued.

巴黎十二大 廖灵敏

报告题目: Polynomial and rational dynamical systems on the field of p-adic numbers and its projective line

报告摘要: Polynomials and rational maps are studied as dynamical systems on the field of p-adic numbers and its projective line. Polynomials with p-adic integer coefficients and rational maps with good reduction are 1-Lipschitz and their dynamical structures are described by a decomposition of the space into finitely many periodic orbits, countably many minimal components and the attracting basins of the aforementioned two parts. For expanding polynomials and rational maps, we can usually find subsystems which are topologically conjugate to subshifts of finite type. The talk is based on a series of works joint with Ai-Hua Fan, Shilei Fan, Yue-Fei Wang and Dan Zhou.

中科院数学所 邱彦奇

报告题目: Patterson-Sullivan construction for point processes and reconstruction of Hardy functions

报告摘要: In joint work with Alexander Bufetov, we show that the classical Patterson-Sullivan construction can be generalized to the random setting in the theory of point processes.  This construction allows us to recover simultaneously the value of any harmonic function in many reproducing kernel Hilbert spaces at any point of the disc from its restriction to a random configuration of the determinant point process with the Bergman kernel. This reconstruction result is then extended to real and complex hyperbolic spaces of higher dimension. Recovering continuous functions by the Patterson-Sullivan construction is also shown to be possible in more general Gromov hyperbolic spaces.

中科院 王跃飞

报告题目： Holomorphic motions and its applications.

报告摘要We talk about quasiconformal geometry and holomorphic motions.  Holomorphic motions were introduced by Mane, Sad and Sullivan in 1980's to solve the density problem of the structural stability of rational maps. Since then holomorphic motions have many important applications in complex dynamics, quasiconformal geometry, Kleinian groups and Teichmuller spaces.

哈尔滨工程大学 衣凤岐

报告题目：Dynamical behaviors of a reaction-diffusion SIR epidemic model describing the population dynamics of fox rabies

报告摘要：In this talk, I will present our recent results on the dynamical behaviors of a class of reaction-diffusion SIR models which are used to model the population dynamics of fox rabies epidemic diseases observed in Europe. To better understand the underlying mechanism of the rabies disease transmissions, we use the “shadow system approach” to study the dynamical behaviors of this particular SIR system. For one hand, we prove that under certain conditions, the time-in-solutions of the original non-degenerate reaction diffusion equations exist globally and remains uniformly bounded; This makes it possible for us to derive a shadow system, which is a degenerate PDE-ODE couple equations with nonlocal term, corresponding to the original system. On the other hand, we are capable of showing that the shadow system is a nice approximation of the original system in the case when the diffusion rates of the infectious individuals are sufficiently large.

中科院应用所 周喆

报告题目：Limit-periodic upper and lower solutions in a generic sense

报告摘要：For a class of second order nonlinear ODEs, we establish limit-periodic upper and lower solutions in a generic sense. This is joint work with M. Tarallo.

大连理工大学 丛洪滋

报告题目：The stability of invariant tori for nonlinear Schrodinger equation

报告摘要：We will study the long time stability of the invariant tori for NLS.