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Friday, April 27, 2018 - 15:05 ,
Location: Skiles 271 ,
Bhanu Kumar ,
GTMath ,
Organizer: Jiaqi Yang

This talk follows Chapter 4 of the well known text by Guckenheimer and Holmes. It is intended to present the theorems on averaging for systems with periodic perturbation, but slow evolution of the solution. Also, a discussion of Melnikov’s method for finding persistence of homoclinic orbits and periodic orbits will also be given. Time permitting, an application to the circular restricted three body problem may also be included.

Friday, April 20, 2018 - 15:05 ,
Location: Skiles 271 ,
Prof. Rafael de la Llave ,
GT Math ,
Organizer: Jiaqi Yang

A well known paper of H. Federer on Flat chains contains a remarkable example attributed to F. Almgren. We intend to give a geometric exposition of the example and explain its relevance in the global theory of geodesic flows and some global problems such as homogenization in quasi-periodic media. This is part of an expository paper with X. Su.

Friday, April 20, 2018 - 15:05 ,
Location: Skiles 271 ,
Prof. Rafael de la Llave ,
GT Math ,
Organizer: Jiaqi Yang
A well known paper of H. Federer on Flat chains contains a remarkable example attributed to F. Almgren. We intend to give a geometric exposition of the example and explain its relevance in the global theory of geodesic flows and some global problems such as homogenization in quasi-periodic media. This is part of an expository paper with X. Su.

Friday, March 16, 2018 - 15:05 ,
Location: Skiles 271 ,
Longmei Shu ,
GT Math ,
Organizer: Jiaqi Yang

Isospectral reductions decrease the dimension of the adjacency matrix
while keeping all the eigenvalues. This is achieved by using rational
functions in the entries of the reduced matrix. I will show how it's
done through an example. I will also discuss about the eigenvectors and
generalized eigenvectors before and after reductions.

Friday, March 2, 2018 - 15:05 ,
Location: Skiles 271 ,
Adrian P. Bustamante ,
Georgia Tech ,
Organizer:

Given a one-parameter family of maps of an interval to itself, one can observe period doubling bifurcations as the parameter is varied. The aspects of those bifurcations which are independent of the choice of a particular one-parameter family are called universal. In this talk we will introduce, heuristically, the so-called Feigenbaun universality and then we'll expose some rigorous results about it.

Friday, February 23, 2018 - 15:00 ,
Location: Skiles 271 ,
Jiaqi Yang ,
GT Math ,
Organizer: Jiaqi Yang

We will present a rigorous proof of non-existence of homotopically non-trivial invariant circles for standard map:x_{n+1}=x_n+y_{n+1}; y_{n+1}=y_n+\frac{k}{2\pi}\sin(2\pi x_n).This a work by J. Mather in 1984.

Friday, February 16, 2018 - 15:00 ,
Location: Skiles 271 ,
Yian Yao ,
GT Math ,
Organizer: Jiaqi Yang

I
will report on the parameterization method for computing normally
hyperbolic invariant tori(NHIT) for diffeomorphisms. To this end, a
Newton-like method for solving the invariance equation based on the
graph transform method will be presented with details.
Some notes on numerical implementations will also be included if time
allows.
This is a work by Marta
Canadell and Alex Haro.

Friday, February 9, 2018 - 15:00 ,
Location: Skiles 271 ,
Joan Gimeno ,
BGSMath-UB ,
Organizer: Jiaqi Yang

We are going to explain how invariant dynamical objects, such as (quasi)periodic orbits, can numerically be computed for Delay Differential Equations as well as their stability. To this end, we will use Automatic Differentiation techniques and iterative linear solvers with appropiate preconditioners. Additionally some numerical experiments will be presented to illustrate the approaches for each of those objects.This is joint work with A. Jorba.

Friday, February 2, 2018 - 15:00 ,
Location: Skiles 271 ,
Gladston Duarte ,
University of Barcelona & GT ,
gladston@maia.ub.es ,
Organizer: Jiaqi Yang

In a given system of
coordinates, the Restricted Three-Body Problem has some interesting
dynamical objects, for instance, equilibrium points, periodic orbits,
etc.
In this work, some connections between the stable and unstable manifolds
of periodic orbits of this system are studied. Such connections let one
explain the movement of Quasi-Hilda comets, which describe an orbit
that sometimes can be approximated by an ellipse of semi-major axis
greater than Jupiter's one, sometimes smaller.
Using a computer algebra system, one can compute an approximation to
those orbits and its manifolds and investigate the above mentioned
connections.
In addition, the Planar Circular model is used as a base for the fitting
of the orbit of comet 39P/Oterma, whose data were collected from the
JPL Horizons system. The possibility of using other models is also
discussed.

Friday, November 17, 2017 - 15:00 ,
Location: Skiles 154 ,
Bhanu Kumar ,
GT Math ,
Organizer:

This lecture will discuss
the stability of perturbations of integrable Hamiltonian systems. A
brief discussion of history, integrability, and the Poincaré
nonintegrability theorem will be followed by the proof of the theorem of
Kolmogorov on persistence of
invariant tori. Time permitting, the problem of small divisors may be
briefly discussed. This lecture wIll follow the slides from the
Satellite Dynamics and Space Missions 2017 summer school held earlier
this semester in Viterbo, Italy.