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 19, Núria Fagella (Universitat Autònoma de Barcelona), TBA

 

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.

 

 

Spring of 2014 Schedule

Fall of 2013 Schedule

Spring of 2013 Schedule