Existence of Quasiperiodic Motions in the realistic N Body Problem

This project mainly concerns Celestial Mechanics and, more concretely, planetary systems.

In broad terms, the main purpose of this project is to prove stability of realistic planetary systems, like the Sun-Jupiter-Saturn.

That is, we want to check that astronomical observations match with the models deduced from the gravitational laws stated by Newton.

The goals will be achieved by a combination of tight theoretical results in KAM theory, tight numerical computations, Computer-Asisted Method and  the parameterization method. This will lead to prove the existence of quasiperiodic solutions for realistic data in the Sun-Jupiter-Saturn system.

More concretely, in this project we will tackle the following problems: - the rigorous existence of Lagrangian and lower dimensional quasiperiodic solutions in both the planar and spatial Sun-Jupiter-Saturn,- the application of all these techniques to other possible (extrasolar) planetary systems.

The results developed in this project will not stop being applicable to planetary systems but also will have a broader spectrum of applications like in models of plasma physics or chemical reactions.A full period of four years will be required to develop this project.En hel period om fyra år kommer att krävas för att utveckla detta projekt.