Speaker : Manuele Santoprete Department of Mathematics, University of California, Irvine

Title: Collisions, Chaos and Periodic Orbits in the Anisotropic Manev Problem

The anisotropic Manev problem describes the planar motion of two bodies under the influence of an anisotropic Newtonian potential with a relativistic correction term. The dynamics of this system is extremely complex, but a glimpse of the global dynamics can be seen studying the collision solutions and the periodic orbits. The flow on and outside the collision manifold will be studied using McGehee coordinates and some features of the collision and near collision orbits will be described. In particular we will show that the presence of a complex, "chaotic", dynamics is strictly related to the collision orbits. This will be done using a suitable generalization of the Melnikov method. Then, invoking a variational principle and using the symmetries of the system, we will find infinitely many classes of periodic orbits.