# Seminario: An integral for the outer average of the secular three-body problem

## Giovedì 19 Maggio 2016, ore 12:00 - Aula 1BC45 - Gabriella Pinzari

ARGOMENTI: Seminari

Giovedì 19 Maggio 2016 alle ore 12:00 in Aula 1BC45, Gabriella Pinzari (Dipartimento di Matematica e Applicazioni “Renato Caccioppoli” - Università degli Studi di Napoli Federico II) terrà un seminario dal titolo “An integral for the outer average of the secular three-body problem”.

Abstract
Poincaré proved that the n-body problem has no other integrals than the energy, the linear momentum and the angular momentum. This strong assertion implies that when the number of bodies is three or more, the problem is not integrable. And in fact most of the ongoing research is devoted to look for orbits exhibiting both stability and instability features. In the case of the planetary problem, namely, when one of the masses is much larger than the others, it makes sense to look at the so-called averaged problem. Again, this problem is not integrable, even though this does not follow from Poincaré's assertion, but
from a recent work by Féjoz and Guardia. The goal of my talk is to prove that a different (“outer”) average of the problem exhibits an integral which is indeed responsible of certain symmetries in the Hamiltonian known in the literature, but, up to now, unexplained. Other applications are foreseen and, if there is time, we shall talk about them.