Title: Computer assisted proofs for non-symmetric planar choreographies
       and for stability of the Eight

Authors: T. Kapela (1) and C. Sim\'o (2)

(1) Jagiellonian University, Institute of Computer Science,
    Nawojki, 11, 30-072 Krak\'ow, Poland.
(2) Dept. de Matem\`{a}tica Aplicada i An\`{a}lisi, Univ. de Barcelona, 
    Gran Via 585, 08007 Barcelona, Spain.
E-mail: kapela@ii.uj.edu.pl, carles@maia.ub.es

Abstract

We present a general method to produce computer assisted proofs of the existence
of choreographies in the N-body problem. This method allows to verify rigorously
numerical data from computer simulations. As an example we use it to prove the 
existence of non-symmetric choreographies with 6 and 7 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.