In this paper, we solved a long standing problem in celestial mechanics. The problem was proposed by Painleve and Poincare in last century. The problem concerns the nature of the singularities in n-body problem and it asks whether there exists a non-collision singularity in the Newtonian n-body problem. Important contributions towards this problem have been made by Painleve, von Zeipel, Moser, Siegel, Saari, Pollard, McGehee, Mather, Devaney, Moeckel and others. Here, we proved the existence of non-collision singularities in the 5-body problem. The method we use includes using McGehee's coordinates both to blow up triple collision singularity and to reduce the dimension of the system. Symbolic dynamics and some other techniques in dynamical system are also employed.
- Pub Date:
- Mathematics, Physics: Astronomy and Astrophysics