Mohammad Zaman, MSc: Integral Manifolds of the Charged Three-Body Problem

Join us for coffee and tea at 15.30 h.

In this talk I report on my PhD thesis entitled Integral Manifolds of the Charged Three-Body Problem. In my thesis I give a mathematical analysis of the physical mechanical system that consists of three charged particles moving in space and interacting via a Coulomb potential. The system is mathematically described by a Hamiltonian on a 18-dimensional phase space. A physical mechanical system may have symmetries and consequently conserved quantities or integrals. From the latter I define a so called integral map. The level sets of the integral map define the integral manifolds. Depending on the values, the integral manifolds may have different topologies. Changes can occur at critical values of the integral map. My main aim is to find these critical values for the charged three-body problem. We will see that besides ‘ordinary’ critical values there are also critical values arising from critical points at infinity and I will explain how to define such points.