**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 (UniversitŽ de Strasbourg et CNRS), TBA

November 5, Yujun Zhu, Dynamics beyond uniform hyperbolicity,
3. Dynamics of partially hyperbolic diffeomorphisms.

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 19, Yunping Jiang, Infinmum of metric entropy for Anosov
diffeomorphisms

and expanding circle endomorphisms preserving Lebegue measure.

November 26, Zhe Wang, On
Weil-Peterssen geometry for Teichmuller
spaces I

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

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