Dynamics and Complex Analysis Research Seminar
Organized by Yunping Jiang (firstname.lastname@example.org) 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, 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.