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Friday, December 7, 2018 - 15:00 ,
Location: Skiles 170 ,
Rafael de la Llave ,
School of Mathematics ,
Organizer: Rafael de la Llave

<p>Given a Hamiltonian system, normally hyperbolic invariant manifolds and their stable and unstable manifolds are important landmarks that organize the long term behaviour.</p>
<p>When the stable and unstable manifolds of a normally hyperbolic invarriant manifold intersect transversaly, there are homoclinic orbits that converge to the manifold both in the future and in the past. Actually, the orbits are asymptotic both in the future and in the past.</p><p>
One can construct approximate orbits of the system by chainging several of these homoclinic excursions.</p>
<p>A recent result with M. Gidea and T. M.-Seara shows that if we consider long enough such excursions, there is a true orbit that follows it. This can be considered as an extension of the classical shadowing theorem, that allows to handle some non-hyperbolic directions</p>

Friday, November 16, 2018 - 15:05 ,
Location: Skiles 156 ,
Sergio Mayorga ,
Georgia Tech ,
Organizer: Jiaqi Yang

In this talk I will begin by discussing the main ideas of mean-field games and then I will introduce one specific model, driven by a smooth hamiltonian with a regularizing potential and no stochastic noise. I will explain what type of solutions can be obtained, and the connection with a notion of Nash equilibrium for a game played by a continuum of players.

Friday, November 9, 2018 - 15:05 ,
Location: Skiles 156 ,
Rui Han ,
Georgia Tech ,
Organizer: Jiaqi Yang

We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. This is a work of A. Avila and J. Bochi. <a href="https://link.springer.com/article/10.1007/BF02785853">https://link.springer.com/article/10.1007/BF02785853</a>

Friday, November 2, 2018 - 15:05 ,
Location: Skiles 156 ,
Yian Yao ,
GT Math ,
Organizer: Jiaqi Yang

The
Shadowing lemma describes the behaviour of pseudo-orbits near a
hyperbolic invariant set. In this talk, I will present an analytic
proof of the shadowing lemma for
discrete flows. This is a work by K. R. Meyer and George R. Sell.

Friday, October 26, 2018 - 15:05 ,
Location: Skiles 156 ,
Jiaqi Yang ,
GT Math ,
Organizer: Jiaqi Yang

Friday, October 26, 2018 - 15:05 ,
Location: Skiles 156 ,
Jiaqi Yang ,
GT Math ,
Organizer: Jiaqi Yang

We show that, if the linearization of a map at a fixed point leaves invariant a spectral subspace, and some non-resonance conditions are satisfied. Then the map leaves invariant a smooth (as smooth as the map) manifold, which is unique among C^L invariant manifolds. Here, L only depends on the spectrum of the linearization. This is based on a work of Prof. Rafael de la Llave.

Friday, October 19, 2018 - 15:05 ,
Location: Skiles 156 ,
Jiaqi Yang ,
GT Math ,
Organizer: Jiaqi Yang
We show that, if the linearization of a map at a fixed point leaves invariant a spectral subspace, and some non-resonance conditions are satisfied. Then the map leaves invariant a smooth (as smooth as the map) manifold, which is unique among C^L invariant manifolds. Here, L only depends on the spectrum of the linearization. This is based on a work of Prof. Rafael de la Llave.

Friday, October 5, 2018 - 15:05 ,
Location: Skiles 156 ,
Adrian P. Bustamante ,
Georgia Tech ,
Organizer: Adrian Perez Bustamante

In this talk I will present a proof of a generalization of a theorem by
Siegel, about the existence of an analytic conjugation between an
analytic map, $f(z)=\Lambda z +\hat{f}(z)$, and a linear map, $\Lambda
z$, in $\mathbb{C}^n$. This proof illustrates a standar technique used
to deal with small divisors problems. I will be following the work of E.
Zehnder. This is a continuation of last week talk.

Friday, September 28, 2018 - 15:05 ,
Location: Skiles 156 ,
Adrian P. Bustamante ,
Georgia Tech ,
Organizer: Adrian Perez Bustamante
In this talk I will present a proof of a generalization of a theorem by
Siegel, about the existence of an analytic conjugation between an
analytic map, $f(z)=\Lambda z +\hat{f}(z)$, and a linear map, $\Lambda
z$, in $\mathbb{C}^n$. This proof illustrates a standar technique used
to deal with small divisors problems. I will be following the work of E.
Zehnder. This is a continuation of last week talk.

Friday, September 21, 2018 - 15:05 ,
Location: Skiles 156 ,
Adrian P. Bustamante ,
Georgia Tech ,
Organizer: Adrian Perez Bustamante

In this talk I will present a proof of a generalization of a theorem by Siegel, about the existence of an analytic conjugation between an analytic map, $f(z)=\Lambda z +\hat{f}(z)$, and a linear map, $\Lambda z$, in $\mathbb{C}^n$. This proof illustrates a standar technique used to deal with small divisors problems. I will be following the work of E. Zehnder.