**Dynamics and Complex Analysis Research Seminar**

Organized by Yunping Jiang (yunping.jiang@qc.cuny.edu) with Linda Keen and Fred Gardiner

Department of Mathematics, CUNY Graduate Center

Fall of 2014 Schedule

Wednesday, 1:30pm-3:00pm (Math Thesis Room, Rm. 4214-03):

September 3, Qualifying Exam (room occupied)

September 10, Tao Chen, Levy Cycles for exponential maps I

September 17, Tao Chen, Levy Cycles for exponential maps II

October 1, Yujun Zhu, Dynamics beyond uniform hyperbolicity, 1. Dynamics of uniformly hyperbolic diffeomorphisms.

October 8, Linda Keen, Dynamics of Entire and transcendental functions I

October 15, Linda Keen, Dynamics of Entire and transcendental functions II

October 22, Yujun Zhu, Dynamics beyond uniform hyperbolicity, 2. Dynamics of non-uniformly hyperbolic diffeomorphisms

October 29, Athanase Papadopoulos (Université de Strasbourg et CNRS), TBA

November 5, Zhe Wang, On Weil-Peterssen geometry for Teichmuller spaces I

November 12, Enrique Pujals (IMPA):

Title: On the density of periodic points and closing lemma.

Abstract: If the positive orbit of a point comes back very close to the initial point,

is it possible to close it, creating a periodic orbit, by a small perturbation of the system?

Pugh proved that this is possible by a C^1-small perturbation and the result

remains widely unknown for higher topologies. We will discuss this problem

with focus on smooth dissipative diffeomorphisms acting on surfaces.

In particular, we will show that for any ergodic measure, either the periodic points

are dense in its support or it is uniquely ergodic and contained in a set semiconjugate

to an irrational rotation. Following that approach some results about the boundary of chaos

for two dimensional dynamics can be obtained.

Disclaimer: no perturbation arguments are used.

Please also note that Prof. Pujals also gives a colloquium talk on Monday, November 10, Einstein Chair Seminar,

everyone in our seminar should go to this talk too.

Title: Generic dynamics: A phenomena/mechanism correspondence

Abstract: Through geometrical models, perturbation techniques and sometimes

analytical approaches, it has been possible to propose and to establish

a dictionary between "a taxonomy of generic dynamical phenomenas" and

a list of "simple mechanisms or dynamical configurations" responsible for

such phenomenas. In an introductory way, I will try to explain the meaning

of such an approach, what is proved in the low differentiability category

and what are the (technical?) obstructions to extend those result to high differentiability.

During next seminar on Wednesday, I will address some results in the direction to bypass such difficulties.

November 26, Yujun Zhu, Dynamics beyond uniform hyperbolicity, 3. Dynamics of partially hyperbolic diffeomorphisms.

December 3, Zhe Wang, On Weil-Peterssen geometry for Teichmuller spaces II

December 10, Sudeb Mitra, Variation of moduli under continuous motions.