Dynamics Seminar

Event Information Magnetic Curvature and Existence of Closed Magnetic Geodesic
14:10 on Monday February 13, 2023
15:00 on Monday February 13, 2023
BA6183, Bahen Center, 40 St. George St.
Valerio Assenza

Universität Heidelberg

A Magnetic System is the toy model for the dynamic of a charged particle moving on a Riemannian Manifold endowed with a magnetic field. Solutions for such systems are called Magnetic Geodesic and preserve the Kinetic Energy. One of the most relevant investigative interest is to understand existence and in case the topological nature of Closed Magnetic Geodesic (periodic solution) on a given level of the energy. I will introduce the Magnetic Curvature, an object which encodes the geometrical properties coming from the Riemannian Curvature structure together with terms of perturbation due to the magnetic interaction. We will see how a positive curved Magnetic System carries a Contractible Closed Magnetic Geodesic for small energies.