The image of a manifold under a map: Invariant manifolds of maps
Abstract: The image of a smooth manifold under a map is the prototypical invariant manifold. The stable and unstable manifolds of a hyperbolic fixed point can be posed as the image of a small part of the stable or unstable eigenspace of the fixed point. Single trajectories (the image of a point) can be computed stably with parallel (or multiple) shooting, and the same formulation can be used with a manifold instead of a single point. For a fixed number of iterates we get a (nonlinear) system whose solution is a manifold.
In this talk I will motivate this formulation and apply it to find a smooth, closed attractor as the image of a nearby manifold with the same topology, and show how higher dimensional unstable manifolds of hyperbolic fixed points can be computed.