| Date | Name |
Title/Abstract |
| January 31 | Joseph Auslander (UM) / David Burguet (Ecole Polytechnique) [double feature] | Local almost periodicity, revisited /
Yomdin-Gromov Algebraic Lemma and dynamical applications |
| February 7 | DMITRY V SCHEGLOV (Penn State) | Title: special flows over IETs.
Abstract: Given a volume - preserving smooth flow on a compact surface with a
finite number of fixed points it can be represented as a special
flow over interval exchange map and a function with symmetric or
asymmetric logarithmic singularities. Mixing properties of these
flows in case of circle rotations were studied in the works of
Kochergin, Arnold, Sinai-Khanin and Lemanchik. The case of IETs of
4,5,6.. intervals remained open. The recent progress was achieved
with the help of deep Diophantine-like properties of Rauzy induction
in the work of C.Ulcigrai (2006) ( asymmetric singularities).
We deal with the case of 4 intervals and symmetric singularities and use combinatorial properties of Rauzy induction.
The talk will include elements of graph combinatorics, Rauzy
induction and substitution systems. |
| February 14 | NO SEMINAR | Valentine's Day |
| February 21 | Gonzalo Contreras (CIMAT) | C2-densely the 2-sphere has an elliptic closed geodesic |
| February 28 | Alex Eskin (University of Chicago) | The Hodge Norm and the Teichmuller geodesic flow |
| March 6 | José Koiller (Courant) | Title: Coupled Map Graphs
Abstract:
We introduce a class of dynamical systems obtained by coupling a
finite number of expanding cicle maps (the "local systems"). The
admitted coupling configurations are quite arbitrary, and most
conveniently described via "coupling graphs" whose vertices represent
the local systems. We show how hyperbolic behavior (uniform or
partial, depending on coupling strenghts) naturally arises in this
setting, and we construct natural invariant measures in some cases.
|
| March 14 2 p.m. - 3 p.m. in room 3206 NOTE THE SPECIAL DAY, PLACE, AND TIME | Jayadev Athreya (Princeton) | Title: Deviation of ergodic averages for billiards in polygons
Abstract: In joint work with Giovanni Forni, we prove a polynomial upper bound for the deviation of ergodic averages for billiard flow in rational-angled polygons. Our main tools are recurrence estimates for Teichmuller geodesic flow.
|
| March 20 | NO SEMINAR | Spring Break/
Semiannual Maryland-Penn State Workshop on Dynamical Systems and
Related Topics in honor of Michael Brin on the occasion of his being
60 (March 15-18) |
| March 27 | Artur Avila (IMPA) | Liouvillean quasiperiodic cocycles |
| April 3 | Frederico Rodriguez-Hertz (IMERL) | Non-uniform measure rigidity |
| April 8 3 p.m.-5 p.m. in room 1308 NOTE THE SPECIAL DAY, TIME, AND PLACE, and that we are having two seminars this week | Elon Lindenstrauss (Princeton) | Stationary measures and equidistribution on the torus
Abstract:
In this talk I will consider actions of non-abelian groups on
n-dimensional tori, explain the notions of stiffness and stationary
measures, and show how under fairly general assumptions stationary
measures can be classified. A key ingredient is a result of Bourgain
related to the sum product phenomena on the reals.
In particular, we prove the following: let A, B be two non commuting 2x2
integer matrices of determinant one. Consider a random product
X_r....X_1.y where y is a point in the two torus. We show that as r->
infinity this random product is distributed in an increasingly uniform
manner.
Based on joint work with Bourgain, Furman and Mozes.
|
| April 10 | Omri Sarig (Penn State) | Title: Equidistribution of horocycles on hyperbolic surfaces of infinite
genus
Abstract: An orbit is called `generic' for a flow on a non-compact
space, if it satisfies the conclusion of the ratio ergodic theorem for
all continuous test functions of compact support and non-zero integral.
Furstenberg, Dani & Smillie, and Burger describe the generic orbits for
horocycle flows on most hyperbolic surfaces of finite genus. I will give
the first characterization of such orbits in an infinite genus setting:
abelian covers of compact surfaces. For such surfaces a horocycle is
generic iff its associated geodesic has an asymptotic cycle, and this
asymptotic cycle is not on the boundary of the set of all possible
asymptotic cycles. (Joint work with B. Schapira)
|
| April 17 | Dmitry Dolgopyat (UM) | Diffusion in piecewise smooth near integrable systems.
I will describe some results and open problems in the theory of picewise
smooth near integrable systems. As an application I will show that a
semicircular outer billiard has an unbounded orbit. |
| April 24 | Kostya Khanin (Toronto) | On exits from an infinite tube.
Abstract: We consider a billiard system in an
infinite tube with periodic scatterers. We show that
with probability 1 a particle exits from the tube.
Surprisingly, the probability that the exit velocity is opposite to
the initial one tends to 1 in a limit when the size of scattereres
vanishes.
|
| May 1 | Maryam Mirzakhani (Princeton) | tba |
| May 8 | John Smillie (Cornell) | Title: Veech groups and lattice surfaces
Abstract: I will explain what lattice surfaces are
and why they are interesting from a dynamical
viewpoint. I will discuss some recent results with
Barak Weiss on characterizing and counting lattice
surfaces. |
| Date | Name |
Title/Abstract |
| September 13 | Mark Kelbert (Swansea University)
| Large-time behaviour of a branching diffusion on a
hyperbolic space |
| September 20 | Vadim Kaloshin (University of
Maryland) | Concrete examples of Arnold diffusion.
Abstract: During the first introductory part I discribe major open
problems and known results concerning Arnold diffusion for nearly
integrable Hamiltonian systems. Then I will present 3 examples of
Arnold diffusion:
The first is coming from the restricted planar circular 3 body
problem and is joint work with A. Delshams and T. Seara,
The other two are elementary and closely related. They are obtained
by concrete perturbations of integrable system:
In the first example diffusion goes along a single resonance (joint
with M. Levi) and
In the second diffusing trajectories can pass through a double
resonance (joint with M. Levi and M. Saprykina). As it is expected
diffusion near the double resonance is faster. |
| September 27 | L. Bunimovich (Georgia Tech)
| MECHANISMS OF CHAOS IN BILLIARDS Two major discoveries of
the last century were the persistence under small perturbations of
chaotic and of regular behavior in dynamical systems. In
typical dynamical systems though these two types of behavior do coexist.
Among the natural questions arising in the studies of such systems
with mixed behavior the following ones will be addressed in this
talk. 1.What are the mechanisms of chaos "compartible" with its
coexistence with regular dynamics? 2.How smooth should be dynamics
to make a purely chaotic motion impossible and to force coexistence?
3.What are types of coexistence of chaotic and regular dynamics? The
new results that will be discussed deal with the studies of
billiards. |
| October 4 | Sheldon Newhouse (Michigan State)
| The structure of two dimensional diffeomorphisms.
Abstract: Recently there is been considerable progress in the study of
one dimensional dynamics. It is natural to ask how much of this
carries over to two dimensional diffeomorphisms. We describe some
ideas in this direction. There are many open problems and several
significant results. |
| October 11 | Giovanni Forni (University of
Maryland) | Title: Remarks on the Greenfield-Wallach and
Katok conjectures
Abstract: We survey recent progress on the Greenfield-Wallach and
Katok conjectures on globally hypoelliptic and, respectively, on
cohomology free vector fields and derive a proof of the conjectures
in dimension three. We recall that a smooth vector field on a closed
connected manifold is called globally hypoelliptic if whenever the
derivative along the flow of a distribution is a smooth function,
then the distribution itself is a smooth function; it is called
cohomology-free if the operator of derivative along the flow has
closed range of codimension one in the space of smooth functions.
The conjectures states that the only examples (up to smooth
conjugacies) are constant coefficients 'Diophantine' vector fields
on tori. The notions of globally hypoelliptic and cohomology free
vector fields where (essentially) proved equivalent in 2000 by Chen
and Chi. Our proof of the Katok conjecture in dimension three is
primarily based on recent work of F. and J. Rodriguez Hertz which
allows us to reduce the question to the case of a Reeb flow for a
contact form. The contact case is settled by invoking the Weinstein
conjecture (which has been recently announced by C. Taubes). |
| October 18 | NO SEMINAR | Workshop on
Dynamical Systems and Related Topics at Penn State |
| October 25 | M. Hochman (Princeton) |
Recursion-theoretic aspects of mulidimensional symbolic dynamics
Abstract: I'll discuss how (elementary) recursion theory can be used
to describe the dynamics of higher dimensional symbolic systems
(shifts of finite type, sofic systems and cellular automata). The
relation between these subjects goes back to Berger's theorem about
the impossibility of deciding whether a shift of finite type is
trivial. Recent work has shown that the language of recursion theory
is suitable for describing both the structure of these systems as
well as other invariants, such as their entropy.
The talk will not assume familiarity with recursion theory. |
| November 1 | Mike Boyle (University of Maryland)
| Subsystems and factors of multidimensional shifts of
finite type: bad examples and the algebraic case |
| November 8 | Alexander Bufetov (Rice
University) | Existence and uniqueness of the measure of
maximal entropy for the Teichmueller flow on the moduli space of
abelian differentials (joint with B.M.Gurevich).
The moduli space of abelian differentials admits a natural Lebesgue
measure class and a natural finite measure in that class, invariant
under the Teichmueller flow. The talk will show this measure to be
the unique measure of maximal entropy for the Teichmueller flow on
our moduli space. The proof proceeds in Veech's space of zippered
rectangles and involves approximation of the Teichmueller flow by a
sequence of suspension flows over countable Bernoulli shifts with
roof functions depending on only one coordinate. This method has
been introduced by Gurevich in the '70's and developed by Gurevich
and Savchenko in the '90's. The uniqueness of the measure of maximal
entropy follows from a result of Buzzi and Sarig (2004).
|
| November 15 | Tere Seara (UPC) |
Exponentially small phenomena: two examples and techniques.
We examine two different examples were exponentially small phenomena
appear: The breakdown of a heteroclinic orbit in some analytic
unfoldings of the Hopf-zero singularity in $R^{3}$ and the
splitting of separatrices of the classical rapidly forced pendulum.
Normal form theory and averaging theory show, respectively, that the
splitting of the invariant manifolds is exponentially small in both
cases. We will review the main tools necessary to give a rigorous
proof of the asymptotic formula for this splitting. In particular,
we will check when the Melnikov integral predicts correctly the
splitting (regular case) and when fails (singular case).
|
| November 22 | NO SEMINAR | Thanksgiving
|
| November 29 | Francois Ledrappier (Notre
Dame) | "Fluctuations of the ergodic sums for some horocycle flows with an
infinite invariant measure"
Abstract:
For conservative ergodic infinite measure preserving systems,
renormalized ergodic Birkhoff sums cannot converge to anything else than
0 or infinity. We give an example where a resummation of suitably
renormalized ergodic sums of an integrable function converge to the
integral. Our example is the horocycle flow on a Z^d cover of a finite
volume surface. I'll discuss the compact case and the new features which
arise in the presence of cusps. This is joint work with Omri Sarig. |
| December 6 | Kristian Bjekloff (Queens University) | Hyperbolicity breakdown in some quasi-periodically forced models
|
