GDP Seminar 2019-2020
2019年09月22日上午10:00    数学与统计学院南研

Non-uniform hyperbolicity in polynomial skew products

The dynamics of Topological Collet-Eckmann rational maps on Riemann sphere are well understood, due to the work of Przytycki, Rivera-Letelier and Smirnov. In this talk we study the dynamics of polynomial skew products of C^2. Let f be a polynomial skew products with an attracting invariant line L such that f restricted on L satisfies Topological Collet-Eckmann condition and a Weak Regularity condition. We show that the the Fatou set of f in the basin of L equals to the union of the basins of attracting cycles, and the Julia set of f in the basin of L has Lebesgue measure zero. As a consequence there are no wandering Fatou components in the basin of L (We remark that for some polynomial skew products with a parabolic invariant line L, there can exist a wandering Fatou component in the basin of L).

冀诸超

Sorbonne Université

2019年09月22日上午10:00    数学与统计学院南研

Steiner symmetrization and its applications in convex geometry

Steiner symmetization was introduced by Steiner in the 18th century. Many (affine) isoperimetric inequalities in convex geometry that characterize ellipsoids can be established by using this approach.  In this talk, we will present some new developments and applications of Steiner’s approach, including the affine inequalities for sets of finite perimeter, and general affine invariances related to Mahler volume.

席东盟

上海大学 理学院

2019年10月10日上午10:00    数学与统计学院南研

A criterion for the existence of physical measures for partially hyperbolic attractors

In the partially hyperbolic setting, Pesin-Sinai showed that Gibbs u-states always exist. However, the existence of physical measures or SRB measures is delicate. In this talk, I will present a criterion for the existence of physical measures for partially hyperbolic attractors with one dimensional center.  The talk is based on a joint work with S. Crovisier and D. Yang.

张金华

北京航空航天大学  ​数学科学学院

2019年11月09日上午10:00    数学与统计学院南研

Variational construction for homoclinic and heteroclinic orbits in the N-center problem

 

It is well-known that the N-center problem is chaotic when N ≥ 3. By regularizing collisions, one can associate the dynamics with a symbolic dynamical system which yields infinitely many periodic and chaotic orbits, possibly with collisions. it is a challenging task to construct chaotic orbits without any collision. In this talk we consider the planar N-center problem with collinear centers and N ≥ 3, and show that, for any fixed nonnegative energy and certain types of periodic free-time minimizers, there are infinitely many collision-free heteroclinic orbits connecting them. Our approach is based on minimization of a normalized action functional over paths within certain topological classes, and the exclusion of collision is based on some recent advances on local deformation methods. This is a joint work with Kuo-Chang Chen.

余国巍

南开大学  ​陈省身数学研究所

2019年11月13日上午10:00    数学与统计学院南研

Dispersion for the discrete operators with absolutely continuous spectrum

In contrast to localization, dispersion for the discrete linear operator with absolutely continuous spectrum is related to some transport properties and the dispersive estimates are important in studying the corresponding nonlinear equations. We recall classical results and present some recent works for discrete Schrödinger operators.

赵之彦

Université Côte d'Azur,​ Laboratoire J.A.Dieudonné

2019年12月19日下午14:30    数学与统计学院南研

Steady concentrated vorticities of the 2-D Euler equation and their stability

In this talk, we will consider the existence and uniqueness of steady concentrated vorticities of the 2-D incompressible Euler equation on smooth bounded domains and study their stability. Given steady non degenerate point vortices configurations, we construct such steady piece wisely constant vortex flows and study their linear stability. Steady concentrated Lipschitz continuous vorticities are also been considered. Both of them are highly concentrated near the given steady vortex points. This talk is mainly based on a joint work with Prof. Yiming Long and Prof. Chongchun Zeng.

王宇辰

华中师范大学 数学统计学院