Hinke Osinga Department of Engineering Mathematics, University of Bristol Computing Global Stable and Unstable Manifolds Thursday 2nd, March 14:05-14:55pm, Carslaw Building Room 173. Dynamical systems theory is a powerful tool to explain how the behaviour of a dynamical system is organised. In particular, many studies involve the investigation of the dynamics near equilibria and how it depends on the system parameters. If one wants to study the global dynamics of a system, it is not enough to merely carry out these local investigations around equilibria. The key components for explaining global dynamics are higher-dimensional objects called stable or unstable manifolds. Even in the simplest examples, these global manifolds must be approximated using numerical computations. If the manifold has dimension larger than one, the computational challenge is substantial and a very active area of research. In this talk I will discuss algorithms for computing two-dimensional manifolds of an equilibrium or periodic orbit of a vector field. I will contrast computing two-dimensional manifolds in the full phase space with computing the associated one-dimensional manifolds in a suitably chosen Poincaré section. A two-dimensional manifold is computed as a collection of approximate geodesic level sets, i.e topological circles, while the computation on the Poincaré section is set up as the continuation of a two-point boundary value problem. My presentation involves many animated illustrations to demonstrate the properties and usefulness of the methods.