Speaker: Arthur Limoge
Title: The twist condition in the three-body problem
Abstract: A famous method for finding periodic orbits of dynamical systems, which we owe to Poincaré, is through fixed point theorems, most of which rely on some form of “twist condition”. In the case of the spatial (circular restricted) three-body problem, this twist condition is a geometric assumption on some 4-dimensional (symplectic) manifold. In this talk, I will describe a conjecture regarding this twist condition whose veracity would yield existence of infinitely many periodic orbits — an open problem to this day. This will be done with a minimum amount of technical details, so that the conjecture can be made accessible to people with little to no background in differential geometry or physics.