Joint BCAM-UPV/EHU Analysis and PDE seminar: The Boundary of Bounded Motions in the Restricted Three Body Problem

LOCATION: BCAM Seminar Room and Online

Abstract
One of the most classical mechanisms generating chaos in Hamiltonian systems is the transverse intersection of the stable and unstable manifolds of a hyperbolic fixed point. In the planar circular restricted three body problem (PCR3BP), the intersection of stable and unstable manifolds associated to fixed points "at infinity" lead to chaotic "oscillatory motions", which leave every bounded region but return infinitely often to some bounded region. Conversely, we can bound motions by searching for invariant tori of the system guaranteed by the K.A.M. theorem.
In this talk we discuss methods to estimate the location of the last invariant torus before the onset of such chaotic motions. Due to the delicate nature of the problem - namely issues coming from the parabolic nature of the fixed point and exponentially small nature of the splitting, careful control of the errors of the associated Hamilton-Jacobi equation are required. The control of such errors are achieved by geometric means. 

Joint work with Amadeu Delshams.

Link to the session: 
https://us06web.zoom.us/j/99649860282?pwd=SE0vemtYMFlwbFBNTXQyOTBONG0vZz09


More info at https://sites.google.com/view/apdebilbao/home