**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),

Title: Non-Euclidean
trigonometric identities and consequences.

Abstract: I will explain geometric
consequences of some identities

between trigonometric formulae in Euclidean and
non-Euclidean geometries.

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, Nishan Chatterjee, Teichmuller space of asymptotical conformal circle homeomoprhisms II