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 2015 Schedule

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


September 9, Organization and Yunping Jiang (Queens College and the Graduate Center, CUNY),

                         Title: Sarnak’s Conjecture and Ergodic Theory

September 16, Jinhua Fan (Nanjing University of Science and Technology),

                         Title: Universal Teichmuller space and BMO Teichmuller spaces

September 23, (No Classes, Yom Kippur)

September 30, Jinhua Fan (Nanjing University of Science and Technology),

                        Title: Complex analytic property of the VMOA Teichmuller spaces


October 7, Tao Chen (LaGuardia Community College, CUNY),

                   Title: Characterization of exponential maps 

October 14, Tao Chen (LaGuardia Community College, CUNY),

                   Title: Characterization of exponential maps, continued

October 21, Enrique Pujals (IMPA and The Graduate Center, CUNY),

                    Title: On a conjecture of Charles Tresser about surfaces diffeomorphisms in the boundary of chaos

                    Abstract: Inspired by his initial studies about the boundary of chaos for 

                                   one-dimensional interval endomorphisms, C. Tresser conjectured that

                                   in the space of C^k orientation preserving embedding of the two disk 

                                   which are area contracting, maps which belongs to the boundary of positive

                                   topological entropy exhibit a period doubling cascade. In a joint work with 

                                   S. Crovisier and C. Tresser we prove such conjecture assuming also 

                                   that the embedding are  in the boundary of zero-entropy systems 

                                   and are ``strongly dissipative". We will relate our results with the problem 

                                   of (topological) renormalization for two-dimensional diffeormorphisms and 

                                   Sharkovskiiś type results.

October 28, Mike Shub (The Graduate Center, CUNY),

                    Title: Periodic point growth rate for smooth maps of S^2?

                    Abstract: This will be an informal talk about the problem of the growth rate of the number of geometrically 

                                   distinct periodic points of smooth self maps on the two sphere of degree two or greater. For

                                   rational maps the situation is clear, but what about smooth maps which share features

                                   of rational maps. For example, maps with finitely many critical points. I must say, not much is

                                   known. Enrique Pujals and I have been discussing the question and we will share some of our thoughts.


November 4, (First talk: 1:30pm-2:45pm) Umberto L. Hryniewicz (Universidade Federal do Rio de Janeiro)

                     Title: Symplectic Dynamics: results and methods

                     Abstract: Recent methods in symplectic geometry have been proven effective

                                     in dynamical applications, prompting Hofer to introduce the term "Symplectic Dynamics".

                                     Among such methods, pseudo-holomorphic curves, which were introduced in

                                    Symplectic Geometry by Gromov, has found inumerous applications.

                                    In this talk I'll discuss the basic ideas behind two kinds of dynamical applications

                                    of pseudo-holomorphic curve theory: the problem of finding periodic trajectories

                                    of Hamiltonian systems, and the problem of finding global surfaces of section

                                    on energy levels.

                     (Second talk: 3:00pm-4:15pm) Pierre Berger (CNRS, Paris XIII (http://www.ihes.fr/~pberger))

                         Title: Generic family with robustly infinitely many sinks

                          Abstract:  Given a manifold $M$ of dimension at least 3, we show the existence of

                                           an open set $U$ of $C^r$ families of diffeomorphisms of $M$ such that there  

                                           exists a Baire residual set $R\subset U$ which satisfies: for every $(f_a)_a \in R$,

                                           for every $\|a\|<1$, the diffeomorphism $f_a$ has infinitely many sinks.


November 11, Linda Keen (Kehman College and the Graduate Center, CUNY),

                    Title: Shell components of transcendental meromorphic functions

November 18, Junyang Gao (China University of Mining and Technology (Beijing)),

                       Title: Some dynamical properties about a family of rational maps concerning renormalization transformation in statistical physics

November 25, Yingqing Xiao (Hunan University), Title: Singular perturbations of the unicritical polynomials with two parameters


December 2 (2pm-3:20pm), Sudeb Mitra (Queens College and the Graduate Center, CUNY),

                                            Title: Some metric properties of Teichmueller space of a closed set in the sphere.


December 9, Fernando Nera Lenarduzzi (IMPA – Brazil),

                      Title: Some results (and examples) on Infinite Ergodic Theory

                      Abstract: In this talk we will talk about Infinite Ergodic Theory,

                                      presenting some results and, through some examples,

                                      we will show how the theory differs from the Classic Ergodic Theory.

                                      I will present a class of maps that are defined on $\mathbb{R}^2$ and preserve

                                      the Lebesgue measure of the whole plane.


December 16, Enrique Pujals (IMPA and the Graduate Center, CUNY), TBA



Spring of 2015 Schedule

Fall of 2014 Schedule

Spring of 2014 Schedule

Fall of 2013 Schedule

Spring of 2013 Schedule