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.
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.
Contact at the MS2Discovery Research Institute: Cristina Stoica and
Manuele Santoprete (Host of the speaker, Tecton 3)
Refreshments will be provided