Lennard Bakker, Brigham Young University
Lennard Bakker is a Professor in the Department of Mathematics at Brigham Young University. He is interested in the existence, through topological means, of symmetric periodic orbits in n-body problems with gravitational interactions, especially periodic orbits that experience regularizable collisions. Other interests are Smale's trivial centralizer problems for maps and flows, and the topological classification problem for hyperbolic total automorphisms.
Singular Periodic Brake Orbits in the Planar Pairwise Symmetric Four-Body Problem
We prove the existence of the periodic brake orbits that experience two distinct regularizable simultaneous binary collisions per period, in the planar pairwise symmetric four-body problem with equal masses and full symmetry among the positions of the four bodies. The analytic existence of the singular periodic brake orbits is based on differential inequalities, qualitative techniques, and the gradient-like flow on the total collision manifold obtained by the blow-up coordinates of McGehee. Before outlining the proof (through many pictures), we review some of the 44 year history of the many applications of McGehee blow-up coordinates to various N-body problems.
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