威尼斯人

（会议时间：2019年1月6日至1月8日）

（会议地点：数学楼二楼学术报告厅）

会议日程

报告摘要

1月7日报告

1、报告题目：Critical covering maps without absolutely continuous invariant probability measure

报告人：Lloyd Simon（Xi’an Jiaotong-Liverpool University）

摘要：We consider the dynamics of smooth covering maps of the circle with a single critical point of inflection type. By directly specifying the combinatorics of the critical orbit, we show that for uncountably many equivalence classes of such maps, there is no periodic attractor nor an ergodic absolutely continuous invariant probability measure. This is a joint work with Edson Vargas.

2 报告题目：Diffeomorphism with a generaliged lipschitz shadowing property

报告人：文晓（北京航空航天大学）

摘要：Pilyugin and Tikhomirov proved that Lipschitz shadowing property implies

the structural stability and Todorov proved a similar result that a Lipschitz two-sided

limit shdowing property also implies structural stability for diffeomorpshisms. In this

talk, we define a general type of the Lipschitz shadowing property which covers the

previous two kinds of Lipschitz shadowing property, and prove that if a diffeomorphism

$f$ of a compact smooth manifold $M$ has this general type of the Lipschitz shadowing

property then it is structurally stable. This is a joint work with Manseob Lee and Jumi Oh.

3 报告题目：Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral center

报告人：张金华（巴黎南大学）

摘要：In this talk, we will present a classification of partially hyperbolic diffeomorphisms with one dimensional neutral center, assuming transitivity. This is a joint work with Christian Bonatti.

4、报告题目：Singularities and C1 robust by Lyapunov stable chain recurrence classes

报告人： da Luz Adriana（北京大学）

摘要：For a differomorphism f of a manifold M we know since [BDP] that if f is robustly (for the C1 topology) transitive in M then it must be volume partial hyperbolic. From the work of [D] and [V], a robustly transitive vector field X on a manifold M can not have singularities. Afterwards the authors prove that this vector fields must have some hyperbolic structure. A natural generalization of being robustly transitive is considering robustly by Lyapunov stable chain recurrent classes. (this chain classes are at the same time quasi attractors and quasi reppelers). In[P] The author shows that this sets have some hyperbolic structure for diffeomorphisms. With Christian Bonatti and Bruno Santiago we show that this chain classes will not have singularities and that therefore they have some hyperbolic structure.

5 报告题目：On the dynamics of bi-Lyapunov stable chain recurrence classes

报告人：王晓东（上海交通大学）

摘要：In this talk, we recall some classical results on (bi-)Lyapunov stable chain recurrence classes. We prove that for generic $f\in \diff^1(M)$, a homoclinic class $H(p)$ is bi-Lyapunov stable if and only if it contains non-empty interior. We also obtain some properties of the boundary of a bi-Lyapunov stable homoclinic class $H(p)$ if it does not coincides with the whole manifold $M$. This is a joint work with S. Crovisier.