## Variational methods and symmetric orbits for the n-body problem

### Davide Ferrario (Università di Milano Bicocca)

created by alberti on 20 Mar 2006

22 mar 2006

Abstract.

Analysis seminar

when: Wednesady, March 22, at 4 pm

where: Sala delle riunioni, Dipartimento di Matematica.

Speaker: Davide Ferrario, Universita' di Milano Bicocca.

title: Variational methods and symmetric orbits for the n-body problem.

abstract: Periodic and quasi-periodic orbits for the $n$-body problem can be found as critical points of the action functional constrained to the space of equivariant loops. Without strong-force assumptions, existence and properties of symmetric collisionless (quasi-)periodic orbits can be proved to exist by such equivariant variational methods, provided the symmetry group fulfills some simple assumptions. As a consequence, global and local optimization numerical techniques can be used to determine and visualize approximations of such periodic orbits.