We present a general method to produce computer assisted proofs of the
existence of choreographies in the N-body problem. This method allows us to
verify rigorously numerical data from computer simulations. As an example
we use it to prove the existence of nonsymmetric choreographies with six and
seven bodies. The method provides estimates for the initial conditions and
for the monodromy matrix of the choreography. These data are used to show
linear stability of the Eight solution restricted to the plane and zero angular
momentum motions.
affiliation:
Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej