**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 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 (Move to December 16 morning 10:30am-12:00noon), Sudeb Mitra (Queens College and
the Graduate Center, CUNY),

Title: Schwarz's lemma and complex geodesics on the 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

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