Geodesic flows and billiards in the presence of magnetic fields

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The aim of this project is to investigate the qualitative behaviour of magnetic geodesic flows and magnetic billiards on compact Riemannian manifolds. In particular, variational methods from Hamiltonian dynamical systems and tools from modern symplectic geometry will be applied to study the dynamics of magnetic fields in smooth compact domains and polygons. Other strands of this project are concerned with rigidity questions for magnetic geodesic flows and the application of symplectic capacities to the study of closed magnetic trajectories.