The Non-collision Sigularities of the 5 body Problem
This paper is a survey on the author’s work on the non-collision singularities in the Newtonian n-body problem. The non-collision singularity in the n-body system corresponds to the solution which blow up to infinity in finite time. The question whether there exists such solution was first raised by Painleve in the last century and since then, it has been open. Here, we show that such solutions do exist in a 5-body problem. The method we use is based on careful analysis of near collisions orbits and McGehee’s technique of blowing up collision singularities.
Unable to display preview. Download preview PDF.
- R. Devaney, Singularities in classical mechanical systems, Ergodic Theory and Dynamical Systems (1981), Birkhauser, Boston.Google Scholar
- J. Mather and R. McGehee, Solutions of the collinear four body problem which become unbounded in finite time, Lecture Notes in Physics 38 (J. Moser, ed.) (1975), 573–597, Springer-Verlag, Berlin Heidelberg New York.Google Scholar
- P. Painlevé, “Leçons sur la théorie analytique des équations différentielles,” A. He- mann, Paris, 1897.Google Scholar
- H. Pollard and D. Saari, Singularities of the n-body problem, II, Inequalities-II (1970), 255–259, Academic Press.Google Scholar
- D. Saari, Singularities of Newtonian gravitational systems, Proceedings of Symposium on Global Analysis, Dynamical Systems and Celestial Mechanics (1971), Brazil, August.Google Scholar
- Z. Xia, The Existence of Non-collision Singularities In Newtonian System, Thesis (1988), Northwestern University.Google Scholar
- H. von Zeipel, Sur les singularités du problème des n corps, Arkiv for Matematik, Astronomi och Fysik 4, 32 (1908), 1–4.Google Scholar