Orateur
Description
In a previous paper written with Ezequiel Maderna, we proved that in the newtonian N-body problem, given a starting configuration x_0 and a limit shape a without collisions denoted as a, there always exists a hyperbolic solution x(t) of the N-body problem such that x(0)=x_0 and x(t)/t converges to a as t tends to +\infty. We will say that x(t) is a hyperbolic motion with limit shape a.
We obtain this solution as a calibrating curve of a weak KAM faible solution, that we call a Busemann function. In this talk i will show that if a is fixed, the Busemann function is unique, up to an additive constant. As a consequence, the set of configurations x_0 where the hyperbolic motion starting from x_0 (and with limit shape a) is unique has full measure in the configuration space.
It is a joint work with Ezequiel Maderna.
