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Towards the proof of diffusion in the Jupiter-Sun restricted three body problem (second, final part)

Tuesday, October 9, 2012 - 16:30 ,
Location: Skiles 06 ,
Maciej Capinski ,
Georgia Tech ,
Organizer:
In the talk we will present a mechanism of diffusion in the Planar Circular Restricted Three Body Problem. The mechanism is similar to the one that appeared in the celebrated work of V. I. Arnold [Dokl. Akad. Nauk SSSR 156 (1964), 9–12]. Arnold conjectured that this phenomenon, usually called Arnold diffusion, appears in the three body problem. The presented method is a step towards a proof of the conjecture. In this second, and final part of the talk, we discuss how to prove transversal intersections of invariant manifolds in the circular problem and how these lead to diffusion in the elliptic problem.

Tuesday, October 2, 2012 - 16:30 ,
Location: Skiles 06 ,
Maciej Capinski ,
Georgia Tech ,
Organizer:

In the talk we will present a mechanism of diffusion in the Planar Circular Restricted Three Body Problem. The mechanism is similar to the one that appeared in the celebrated work of V. I. Arnold [Dokl. Akad. Nauk SSSR 156 (1964), 9–12]. Arnold conjectured that this phenomenon, usually called Arnold diffusion, appears in the three body problem. The presented method is a step towards a proof of the conjecture.

Wednesday, September 19, 2012 - 16:00 ,
Location: Skiles 06 ,
Lei Zhang ,
Georgia Tech ,
Organizer: Rafael de la Llave

Continuation of the exposition of N. Fenichel classical paper on the persistence of Normally Hyperbolic invariant manifolds.

Wednesday, September 12, 2012 - 16:00 ,
Location: Skiles 06 ,
Lei Zhang ,
Georgia Institute of technology ,
Organizer: Rafael de la Llave

We will present the classical work of N. Fenichel on persitence of overflowing manifolds.

Wednesday, September 5, 2012 - 16:00 ,
Location: Skiles 06 ,
Rafael de la Llave ,
Georgia Institute of technology ,
Organizer: Rafael de la Llave

We will present a classical proof of the center stable manifold.

Wednesday, August 22, 2012 - 15:00 ,
Location: Skiles 0t ,
T. Bartsch ,
Univ of Loughborough ,
Organizer: Rafael de la Llave

Thursday, May 3, 2012 - 16:00 ,
Location: Skiles 006 ,
Alan Diaz ,
Georgia Tech. ,
Organizer: Rafael de la Llave

In this introductory talk, we review the dynamical motivation for definingsymplectic manifolds, then describe a class of invariants called symplecticcapacities, which are closely related to both volume and the existence ofperiodic orbits. We explore the connections and differences between thesethree notions in the context of some basic phenomena/problems in symplecticgeometry: Gromov's nonsqueezing theorem, the difference between symplecticand volume-preserving diffeomorphisms, and the question of existence ofclosed characteristics on energy surfaces.

Wednesday, April 11, 2012 - 16:00 ,
Location: Skiles 005 ,
Mikel J. De Viana ,
Georgia Tech. ,
Organizer: Rafael de la Llave

In the 1990's Marina Ratner published a famous series of papers showing that ergodic measures invariant under unipotent flows over quotients $\Gamma/G$ are homogeneous. From this, she deduced many other remarkable properties for these flows (e.g that the closure of orbits are homogeneous and that orbits are uniformly distributed in their closures). To prove this result will require several lectures, but already the case of horocycle flow in $\Gamma/SL(2, \mathbb{R})$ presents several or her ideas. In this talk we will present the ideas of the proof in this case and present an application due to Margulis.